Giza (09:00)-Luxor (10:10) M, Th, Sa
Luxor (10:40)-Giza (11:50) M, Th, Sa
Giza (17:00)-Luxor (18:10) M, Th, Sa
Luxor (18:40)-Giza (19:50) M, Th, Sa
Assuming that the operation at SPX is similar to that at Abu Simbel then one could assume 30 minutes would be sufficient for check-in and arrival checks. The planes seat 75, and the airport capacity is listed as 300 pax/hr.
I attach some pictures taken from Google Maps that put the distances into perspective. Traffic jams on the Alexandria Desert Road (75) seem to be the major problem. The distance from SPX to the pyramids, passing GEM on the way, is about 20 miles or 30 kilometers, so about 30 minutes.
Aswan started with 2 flights on Friday, one of which continued to Abu Simbel, and one on Wednesday.
Sharm el-Sheikh starts with one flight each way on Thursday, Saturday and Sunday.