[Radek]

That's weird. I am always able to do it. The flask is okay, both the flasks from the chest and the flasks from the "kitchen" work. Also it is possible to put the flask on the grill both from your inventory and from your "pockets". Perhaps, only one overlooking could make problems. The flask must be "used", not "given".
Therefore, select "use", then select the empty flask on your list and then traverse the grill with your mouse. Click, once you see a blue cursor. The flask should occur on the grill. If it isn't then the game is corrupted somehow.