Shit, I don't really know what else you can do to run .swf files on Android these days. But .apk files should run on their own I'd say, being 'native apps' for the OS.
- There once was Flash Player for Android 4, maybe useable in Android 5. Guess it's outdated and insecure, as is old Android.
- Some web browsers for Android are based on Chromium, they include a more recent Flash Player component.
(Google e.g. is updating the Flash component for all their browsers iirc, not sure for Android, please check that.)
Try one browser that explicitely mentions Flash support. Also check updates, especially for the Flash component, recent version number of Flash is 32 afaik. I found Puffin Browser, Dolphin Browser, Photon Flash Player & Browser... Sadly there is not too much to recommend. As long as you download from proper sources and only use Flash for games the security risk should be minimised.
Hope this helps somewhat, please report back with the solution that works for you. I'd like to know myself. :/