Ndtyhij

It is probably possible to come up with in-game reasoning, but to my ears they sound contrived and might have adverse effects on the rest of your game, so I won't bother. ("But wait, if that's true, then why can't we just...?" and the next thing you know they've invented blood-tracking stirge-artillery or something out of genre.)

However, out-of-game, a public statement in front of other players such as, "Look, it's a standard piece of adventuring equipment, and I don't want to get too far into the weeds with justifications about why it's safe. But I will say, publicly, that I will never have one of these things randomly shatter and incinerate on you without warning. Normal adventuring won't break them, and if you're doing something that would stress it, I will warn you."

A public GM declaration of "I'm not going to screw with you over this," really ought to be good enough. If it isn't, you're treading on your player's suspension of disbelief, and maybe shouldn't press it much harder unless you have a good reason. Let the player play his character.

It's probably assumed that adventurers aren't just chucking the fragile glass container directly into their backpack with all their other stuff, but put them in a safer container and remove it when it needs to be thrown at something.

Sliding the flask into a form-fitting metal container or wrapping it inside your bedroll should make it pretty resilient to accidental impacts. Once you get to the point where enough crushing force is applied to you that the flask can break through your bedroll or its protective covering, you probably have more pressing concerns than the flask shattering.

Carrying adventuring gear is always a trade-off between risk and reward; wearing a full plate armor also introduces some risks when you travel near the water. Still, most adventurers would prefer taking the risk of falling in the water over the risk of being in combat without their armor.

Likewise with Alchemist's Fire. Sure, there's some risk to carrying it (which you'll want to mitigate with protection) but would you rather be in a situation where it hurts you, or in a situation where you desperately needed it to hurt something else, but refused to bring it for its risk?

I agree that you should probably just say out of game: "As the DM I am not going to let it break, just like you are not going to hurt yourself on the 5 swords you carry in your backpack."

But, I would add that if your players really care about that stuff, then you can also just accept it. If they want to track how all their equipment (and loot) is stored, let them do it. But I would put the work on them. They tell you how it's stored. If they think there was a chance for the alchemist's fire to break because of something they did, they can roll themselves to check it. If they don't want to use alchemist's fire because of it, so be it.

Why not let them play their character authentically?

That's a great personality trait to use as part of a plot development. Their hyper vigilance and over-concern for minor issues can be a great addition to the game.

I GMed with a player with a Bard who (like the player) had a hard time paying attention. Every time the group was being stealthy he would start singing songs and playing his flute "quietly." At first it was frustrating, but after changing the course of the game several times I and the other players came to appreciate his "flaw." We all got a lot of laughs and he became very proud of his "adhd bard."

Let the player worry about the bottles breaking and adjust your story telling accordingly.

By the way, that bard ended up being the only player in the party not captured by the minions of evil near the end of the campaign. He had everything he needed to free his companions but of course he had to roll three separate stealth checks. Everyone was holding their breaths as I narrated and he snuck around, and he did it! Without once singing or playing his flute. It was one of those moderately exciting moments that ended up being totally epic and gripping, and it was all because this player had to overcome a real character flaw.

The simple answer is "it's up to the DM". If the player is comfortable enough carrying around glass bottles of healing potion and not worrying if they break, then they shouldn't worry about the vial of alchemist's fire. If you have a history of breaking potions in their bags if they botch a roll, then it's a very rational fear.

You're the DM. YOU are the one who decides if anything will crack the vial. And the vial will not crack unless the DM says it does. If you say it won't crack, it doesn't matter if the player powerbombs it off a mountain into a lake of nitroglycerin.

You can also specify what situations WOULD crack the vial (rolling a 1 on an acrobatics check for fall damage, the player being hit with enough damage, etc).

If you really want to have fun with it, you can have them make a dex check to put it in a sturdy metal thermos or something. When the time comes to use it, the player throws it out like a flamethrower rather than an incendiary grenade.

Simplest answer:

You all are overthinking it. Just don’t worry about it, right? Right? (I mean, I can’t even do that, I’m literally sitting here writing up an answer to the question! Not sure why I’m suggesting it ;)

Not so simple answer:

It’s important to remember, and each rule book points this out: the rules (and the world itself) are at the discretion of the DM. So you don’t really need an answer that is based on existing canon of any sort (not that you were necessarily looking for one. Just wanted to make that clear for anyone else reading this.)

I think a simple, fairly logical solution is to make up a little lore that explains that the flask works like unto a grenade. Ie., the flask has to be “armed” in order for it to go off. How you want it to be armed is really up to you. Maybe there’s a ribbon to pull? Maybe you have to say a code word? Granted, these would add some new rules...since you suddenly have a physical or verbal component ;). The cleanest solution would be to say that the trigger is psychic. Ie., the bottle literally is designed to know who is throwing it and will not arm itself until after it’s been thrown.

Any of these explanations could work. But, beware, as has been noted elsewhere: anytime you start to add lore, there’s going to be a chance that the players will extrapolate that lore into other situations. Some DMs frown on that but....I dunno, I really enjoy it when my players push my logic back at me. I enjoy working with the players on my own bullsh*t to make the game more fun. And in the end, that’s what we’re after, eh?

You want an in-game solution? The shop that sells Alchemist's Fire also sells the containers that are specifically designed to safely contain the vials (while making them easy to remove so they can be thrown as a single attack), sort of like the gun-powder containers found on old battle-ships.

Since everybody uses these, any Alchemists's fire recovered as "loot" will also be contained in these containers.

Depending on the style of your game you might allow this role-play just for fun. Maybe this player is not interested in using that item at all. Like others have answered, the correct way would be to tell them out of game that you won't screw them like this.

But I want to consider another way of seeing it.
Let me give you an example of similar behavior:

Once in a game of 5e, my character (knows how to swim) fell in deep water. My character, afraid of drowning, chose to drop his sword, bow, boots and other things in order to swim out safely. Now the rules technically, I believe, only say that full-plate will be a problem when swimming, I could have kept the sword and everything according to the rules. However I'm not about min-maxing or something like that, for me the fun is in the role playing so I chose to do that, even if the rules favorised min-maxing (keeping my stuff), because I felt that is how my character would think. (swimming with a sword in hand ? no thanks) I still had some daggers and options, and a replacement weapon is not hard to find, since the equipment wasn't anything precious. It was also funny, since everyone knew I didn't have to drop my sword.

As advised by user lightcat: let them play their character authentically

Your player probably understood that the alchemist's fire is supposed to be safe in game and that such safety consideration can be largely overlooked by players, however he chose to push the realism a bit more far, and he's also developping the personality of his character, a careful, smart, pragmatic character. That's their choice, I think to "convince" the player otherwise is not the right move here. However if they do want the flask, you can reassure them it won't be dangerous.

This is a situation of realism/role-play VS game mechanics. The beautiful thing about DnD is that it allows role-play to transcend "game mechanics".

If your player does not accept an out-of-character answer, like Novak's, offer an in-character solution. In the next item shop they find armoured bandoliers for sale, with several (whatever number you think is reasonable) padded steel cylinders that neatly fit one alchemist's fire flask (or acid flask, or holy water, or...) in each can. Perhaps the shopkeeper demonstrates by putting a delicate glass rose in one, and chucking it across the room.

Make it fairly cheap (1gp?), and don't penalise the player for using it (don't force them to use an action to draw a flask from a cylinder), and hopefully the player will accept that their character is now convinced.

I think this is better than just telling them that their backpack is secure enough, because it allows the player and character to take a deliberate action to ensure their safety. I think they will thus find it a bit more convincing.