in my experience, if you need to rewrite the outcoming links in order to strip the extension and then cache the page with the extension in order to use the standard configuration of the flush Agent, you just only need to apply the strip configuration from the Link Checker Transformer configuration and apply a rewrite at the apache level in order to add the .html extension for the incoming request.
In that way the extension is applied in the cache and you don't need to change nothing into the Flush Agent.
There are several solutions but that depends on your "requirements". You'll find a lot of threads in this forum itself -
You'd have to do a lot of custom effort to strip .html in web server then map it back to content using sling mappings for sling to resolve it. Post that, you'd have to write custom flush agents to manipulate the path where you plan to utilize it.