I live in a tiny town about 10 miles from a town witha pop. of 12,000. Couldn't find upholstrey foam ANYWHERE. I ended up using 1/8 inch thick underlayment foam that i had left over from my hardwood floor when i redid the kitchen. It worked out perfectly but i had to cut out two sets of flames and glue them together. I used regular 3m super adhesive spay available at any auto parts store.
Also worth mentioning this is a 1/4 inch thick foam backed headliner, that i got at the local fabric shop. (12 bucks) when i ordered one from paddock it was like $30 plus shipping and was only 1/8 inch thick foam backing. So if you go that route you may only need 1/8 inch foam for whatever 3D design you use, or you could go 1/4 inch and really have it pop out at you.
the bottom four inches of my flames is only 1/8 inch foam and then it's 1/4, so the flames kinda taper up where they start. but you can see the 1/8 inch area really good actually. so you may even be able to do 1/8 inch foam with the 1/4 headliner for a very subtle look. Oh and don't forget where your sunvisors go when doing your design! I had mine set out so i could see where they'd go and didn't cover much up.
put it in a few days ago, nice finally having a headliner and interior plastic again

not to mention sunvisors. made it feel like a whole different car inside, way less road noise. lol.