My question is, can you use singleton classes with mobile apps?
Yes. There is no problem at all using a Singleton. Your problem has to do with loading a SWF at runtime. Instead of loading it with a Loader, turn it into a library asset so the class can get linked in during the compile process.
I don't want to compile these SWF's. I am loading them dynamically at runtime. They will be changing all the time, I cannot compile them into an app.
The point I am making is that there seems to be a bug in the way Flash Builder is comiling for iPad. It seems to think I am compiling a SWF file that has code on the timeline. I am clearly not doing this, it is bizarre adn makes no sense. I will be testing this on an Android device soon and I am 100% confident it will work. It is an iOS packager bug, I am fairly confident of this.
It's not a bug. The iOS developer guidelines prohibit anything compiled to be loaded at runtime. Thus, there is no port for the Loader class in the cross compiler.
You need to take it up with Apple (fat chance), not Adobe.