I just don't see this working. I worked in L.A. for eight years at the Coliseum when the Raiders were there.
Unless the teams are dominant winners, LA cannot and will not support 2 teams. Even when the Raiders were good, we only averaged about 60,000 in attendance in a stadium that held over 90,000. The Rams certainly did not draw any more than that.
The Charges would be smart to try and build their own stadium in Orange County, the Valley, or downtown L.A., in that order, imho. Orange would be the best bet because of the population and the money that is in that area. The Valley would make sense because of population and access to Simi Valley and Ventura.
If in the end they are just sharing the new stadium in Inglewood, I don't think that will last long. So far, I guess sharing Staples is working for the Lakers and Clippers, but not sure it would work for football. Hell, even USC and UCLA didn't want to share the Coliseum. Of course, the Rams were playing there too back then.
It will be fun to watch.