Since I am sure NBC payed a pretty penny for the right to first flex, they should get first pick. ESPN would get the second pick.
I suspect that CBS and FOX would likely object as they would lose 2 of their prime matchups.
But maybe the pick order could be determined by a hat with NBC, ESPN and the double header network getting the first 3 picks in a random order. This would probably never fly with the networks.
It's interesting you mention this. ESPN is actually paying about twice as much for Monday Night Football than NBC is paying for Sunday Night Football. ESPN is paying $1.1 billion a year, while NBC is paying $600 million a season. CBS & Fox are paying $1.3 billion a season. So, the network paying the least (NBC) has flexing abilities, plus gets to televise the Super Bowl twice during the length of their contract.
The way it's set up, from weeks 10 through 16, CBS & Fox are able to protect 5 games each, but it can't be 2 games in the same week. They're not allowed to protect any games for the final weekend of the season. By the wayl, CBS & Fox have to let the league know after the 4th week of the season which games they wish to protect.