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".