Yeah, a lot of overlapped things will z-fight/flicker. The only remedy is to move 1 of the pieces a pixel or 2 up or down. This is easy enough with non-gridded parts like most wall trim, windows, signs, etc. However, it's a bit trickier with gridded parts like the flat roof pieces.
With them, you have to select 1 of the 2 pieces that overlaps, then hit the button to separate that piece from the building. This creates a new building with only that 1 piece in it. Deselect everything, then select the new 1-piece building. On the level of the whole building, before you get into editing individual pieces, you can hit X to Advanced Move the whole building, which in this case is just the 1 piece. Do that and move the "building" just 1 or 2 pixels up or down. That will solve the problem.
HOWEVER, I recommend only doing this as the very last step of constructing that building. Once the piece is in a separate building, it makes doing major changes to the whole building a bit more complicated. So with me, when I do my last pass through a building to make sure I put all the trim everywhere and didn't accidentally delete part of it with a stray right-click, I also get rid of all the z-fighting like this.