How do you get a big mushroom in FireRed?

i do believe you can steal them from paras and parasect. its rare that you'll get a big mushroom though (you mostly get small mushrooms)

the best way to do this though is to get some parasects and parases in the safari zone. it is about 90% of chance of them having either two tiny mushrooms or a big mushroom. the reason I say 90% is because I never caught a paras or parasect without them have a mushroom or two
paras and parasect will sometimes be holding mushrooms ( big and little).
Paris sometimes have mushrooms as an item in the wild. either catch them and hope they have small mushrooms or use the move thief to steal them, if they have them that is. Paris are everywhere but there are alot of weak ones in mount moon