Just to elaborate a little further, correct, you don't have to use Edge.
Also, Captivate can bring in .oam files (Edge animate, as you know) or .zip files.
I created a Canvas document in Flash Professional with a simple animation and published (publishes to HTML5 format).
Then I went and manually zipped together the resulting files.
They imported into Captivate using Media>HTML5 animation just fine.
Alternatively, you can take your HTML5 files that make up your animations (outputted from Flash Canvas document, or whatever software you're using) and put up on a webserver. Then, grab that URL, and back in Captivate, go to Interactions>Learning Interactions, scroll to the bottom and choose WebObject. Paste the URL in, preview HTML5 in browser, and you'll see it.
Kind of veering off your original post, for those with Flash expertise that need HTML5 animation, using the Canvas document type in Flash will create that HTML5 friendly format that you need.
If you have swf-based animations in a .fla that you need converted to HTML5, you can even copy and paste from a traditional .fla Flash file (that outputs to swf) into a Flash .fla (Canvas) document. It converts over pretty well, although if you have actionscript, it's commented out. For some animations it could be a great way to get swf-based ones converted to HTML5 quickly without having to re-build the whole thing.