I can attest that both IE 10 and 11 and Edge flash updates are covered by Windows Update in Windows 10.
HTML5 is not yet available for Edge at this time and the flash version used in Edge is the active-X version. Hope this helps.
As far as using the avast software updater directly, I don't do that, but go instead directly to the vendor's site to get the updated file required. Doesn't matter what is reported as insecure, procedure is the same for all.