If it's packing foam, it probably isn't fire retardant. If it's furniture foam, it might be.
The fire that killed 100 people at a Great White concert a while back was fueled primarily by packing foam hung on the walls.
Either way, the acoustic properties of the foam aren't going to do much for you. It might shave a bit off the very high frequencies, but it wont do anything for the low freqs where most recording problems are.
Small booths are good for vocals, as you want vocal recording to be as "dead" as possible. Isolating the booth (as opposed to acoustically treating it) is a matter of adding density. Make the walls as thick as you can with the densest material you can find. If isolation isn't at issue, then buy good quality acoustic foam (designed for purpose) and deaden the room as much as possible. Since the space is too small to ever give you that "live" sound, go the other way, get the dead sound as much as you can, and then treat the recording in post-processing.
Just how much space in the shed are we talking about?
Someday we'll win this thing...