I don't know if Flash has a memory limit of its own. The memory for your Flash file is based on the available memory on your computer.
There is a limit on the number of frames that you can have in any given timeline. I think that it's about 15000 frames, but that's a guess. Flash does all of its work at runtime, this means that no part of your animation is pre-compiled like it is in a video file. So the more objects that you have on the stage, the more work Flash has to do. It follows that the more objects that there are to animate, the more work your processor and the video card have to do.
Here's a list of articles on memory management that might be useful:
Garbage collection internals for Flash Player and Adobe AIR | AdobeDeveloper Connection
actionscript 3 - What are good memory management techniques in Flash/as3 - Stack Overflow