Josh helped me out yesterday on TS, and it looks as if it's all solved! It was all about CoD4 graphics settings. As I had most of my settings off, we turned many of them on again, which removed entirely the flickering. It became very laggy and difficult to play though, so I set again some settings to off, one by one. At the end I only had Dual video cards and Sync every frame on. Still quite a lot of lag. I turned Sync every frame off, which removed pretty much all lag and doubled my FPS. A tiny, tiny flickering came back with that, but occurring much more seldom than before, and nowhere near as annoying. I can live with that.
Thank you @FunkyJosh>XI< !
@Oster I haven't had the occasion to use the community patch before Josh took me through these settings, and now that the problem is solved I'll keep it that way. Thanks for the tip though!