How can I run an EXE Flash App on my android device? Basically I have an EXE file that executes a lot of SWF files in another folder running an interactive slideshow type thing.

Is there anyway that I can de-compile the EXE file or something in such a way that I can execute it to run the slideshow on my android device?
That's a big "Probably not". Even if you could replace the EXE, you run into the fact that Android hasn't supported Flash officially in a few years.

If you want to just run the SWF's without the EXE, you can still manually install Adobe Flash Player together with SWF Player, but compatibility these days is probably hit-or-miss (mostly misses I believe). If it does work on your device, interactive SWF's may have problems. 

But if it's worth a shot, it's worth a shot.