Red and black flags
2 countries have a red and black flag, with no other significant colour: Albania, Angola. 30 other flags also contain these colours, plus others.
Red and black, plus other colours
Other colour combinations
red, white and bluered and whitered, green and yellowred, white and greenred, blue and yellowwhite and blueblue and yellowred, white, green and blackred and greenred, yellow and blackblue, green and yellowwhite, blue and greenred and yellowwhite, green and orangered, white and blackred, white, blue and greenred and bluered, white, blue and blackred, blue and greenred, white, green and yellowwhite, blue and blackred, blue, green and yellowred, green and blackwhite and greenred, green, yellow and black