Question: I have Flash files that I would like to make edits on but I don't know how or with what.

Is there some software that can edit a Flash (.fla) file?

(Ideally something free.)

Answer: 
You can install the free 1 month trail version of [Adobe Flash CS4 Professional](https://www.adobe.com/products/flash/), which you can use to edit and create free flash movies. If all you need to do is a one-time editing of the flash (.fla) file, you can get away using just the trial version.
there are no legally free programs that allows full capable editing of Flash source files (.fla). Only Adobe Flash (not Player!) can do it.

I suggest you stop wasting time hoping a free program like this comes along, and start using that time saved to work and buy a copy eventually.