If everything had to be flame-retardant then we couldn't even put up posters or maps, or anything made from paper!! I haven't heard that before, and schools certainly don't follow that.

Safety is an important thing to think about though. The exits need to remain clear, and having a lot of fabric hanging down could cause tripping, and possibly a fire hazard. But if you keep safety at the front of your mind when you are building your tent area, then you should do OK.
I personally would not set up a real tent in a room long term, they get stuffy and could be a safety hazard if you all had to leave quickly. The simpler the better, in my opinion. We've set up tents temporarily for VBS, and they really can "get in the way" if your space isn't large enough, and they are hard to get in and out of with a big group.

Since you can't hang things from your ceiling, what about using PVC pipe to build a frame so the posts can be right up against a wall. That should easily hold the fabic and then you can make sure the door of your "tent" is large and open for easy access and exiting.

Just some thoughts.