Drastic solution would be .gif animations.

You could also make them flash animations become video files and upload them on Google Drive?

I am surprised that they haven't started doing videos here on furaffinity. There isn't a video for furries only streaming site is there?

Think what I've seen is including ANIMATION in the title and then using a still from it, then linking the animation on e6

There's tons of programs that can just convert Flash to something like MP4, MPG, OGG or whatever video format you'd like to have. Google will probably show you thousands of those, so beware that you don't stumble into any malware. But for simple, looping videos, converting Flash animations/video to just plain video files should be easy. Many standalone video encoders have an option to load and render Flash into a video, as well. (Pretty sure even a few of Adobe's own programs will do this.)

It's worth noting that Flash Video is simply a container file that holds an encoded video file, anyway. You can probably just extract the video (usually VP6, Spark or H.264) without any recompressing.
Try https://www.videohelp.com/software/FLV-Extract or any other de/re-muxer that can process FLV.