I have the same problem using only the integrated graphics (HD Graphics 4600).
Starting Civilization V with DX11 in fullscreen makes my display (DELL U2414H) to switch from 1920x1080 to 1080i and showing screen flicker.
If I run the game in windowed mode it shows no flicker, because it stays in the same 1920x1080 (p) mode like the desktop.
Starting Civilization V with DX9 the fullscreen mode works without any flicker, it then runs in 1920x1080 (p).
The display is connected via DisplayPort and shows the same behavior using HDMI or DVI to HDMI.