Will Connect still work as an LMS after Flash is retired?

It's also worth mentioning that the underlying technology that Connect is built on will still be in place after the end of 2020 (at least that is the plan I've seen for now). So, the Flash based presentations may still be uploaded to and delivered from Connect, but the issue is more around a lack of browser support for that content.

As Tom mentioned, Adobe's authoring tools now have HTML output options, and it may be prudent to begin authoring training content that way starting now to avoid a scramble to re-author all your content at the last minute to ensure your learners can still access the content easily.

Flash support is being retired.  Some people will likely still utilize Flash, but Adobe is moving everything from authoring tools and Connect to HTML5. Can you publish your content as a zip package with both HTML5 and Flash instead to future proof it?  That option is available in the last few versions of their authoring tools.