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.
You can download the 30-day trial version of [Adobe Flash Professional](http://www.adobe.com/products/flash/). I don't know of any free alternative that works as well.