Due to the unclear sovereignity over these two areas, I intended to design "neutral" flags, that could be used by the two sides indistinctly. Both flags used pan-Arab colors.
For Bir-Tawil, I made the following design:
Both Egypt and Sudan use red-white-black (in this exact order) horizontal tricolor flags. The white trapezium represents the shape of the area and its location between the two countries. Red represents the Egyptian desert, as the Ancient Egyptians used to distinguish the black, floodable "black land" from the desertic "red land". Black represents Sudan's name etymology, "black man".
The Hala'ib Triangle flag has the geometrical shape that the area its name:
As explained for the previous flag, the black color represents both Sudan and the fertile Egypt. The red stripe in the fly represents the Red Sea. The triangle is obvious.
I think the result was two unique flags, but still very simple.
Comments and suggestions are welcome.
Please, no politics on the comments.