What causes this white coloration of the ground in Gilf-Kebir?
The white areas appear to be formed on the edge of elevated parts of the landscape and in low-lying flat areas. You can see this if you use Google Earth and looking at the elevation profiles along paths you sketch across the landscape. They don't appear to form at a particular elevation or other pattern that would indicate they are bedrock outcrops.

I think the most likely possibility is that they are caliche deposits (calcium-carbonate cemented sediments), formed as water ran off of higher elevations, mobilizing calcium and evaporating to cause calcite saturation. They could be halite but I would expect more extensive deposits in the broader drainage areas if they were salt. They could have formed under wetter climate conditions. If you look at 23 degrees 14.053' North, 24 degrees 25.22' East, you can see deposits being covered by sand dunes.