OK, looks like I got it.
I’m not sure what did the trick but what I did was setting the field options to anti flickering. I did it for the solid and it really stopped flickering. The other thing was that I have set the fps to 29.97. The 720p footage still flickers a little but then again, can it be because of a 720p video being in a FULL HD one (its scale is a little higher but it still covers only a part of the 1920×1080 result video.)