I have used an A1200 with the 'internal' Scan-Doubler (I forget who makes it, it clips onto a chip on the mobo, and a ribbon cable connects to a unboxed 'dongle' that plugs into the DB23 socket and provided a DB15 socket for a VGA monitor) and have connected it to an IBM 640x480 12" LCD flat screen.
It flickered badly. There were dropped pixels all over the screen, fickering randomly on and off, a bit like snow that you get on a bad tv picture. My guess is that the Scan Doubler only doubles up to 29hz or whatever, and thats a bit too low for the screen.
The scan doubler works fine on any other CRT monitor however.
-Jar.