Use the fla files as any other binary file - you will have to overwrite from the latest version or produce a merge manually. There is no other choice when using subversion.
This is what I would do:
Lock the fla files in the branch so that noone overwrites them, this way you don't need to try to compare two fla files that each have been changed. (Explain this to the team, locking in SVN can undone, it's more a reminder than an absolute stop) Instead of changing the fla files add new ones with the replacement functionality, add comments during commit on how these changes could be included in the main fla files.
Split the fla files into multiple smaller ones so you can isolate the changes more easily.
Make sure that commits of fla files are always accompanied by a good commit message that describes what was changed.
Move as much as possible out of the fla's -- images can be embedded using code, and of course no source code should be in the fla.
Make sure everyone on the team knows about the issues with subversion and binary files.
It's not perfect, but this will keep it somewhat manageable.