Hi,
It is a complex question, right now only Edge Dev on Windows 10 Insider preview is supported in Kiosk mode. microsoft-edge-configure-kiosk-mode
So for now Edge Legacy is the choice...
When it is ready you will be able to configure it using the PowersShell MDM Bridge, here is an example windows-10-1809-kiosk-mode-with-an-ad-domain-account
As soon it is supported with Edge Chromium I will update it.
Regards;
Jörgen