in Sinquefield Cup how is white player determined? Do they flip a coin to determine white player? Does the person in that round who has higher points choose? Do they rotate (and if so, how is the first round white player determined)?
In round-robin tournaments, the schedule is known in advance. A very common schedule for 10 players starts with the following games in the first rounds:

Round 1: 1-10 2-9 3-8 4-7 5-6
Round 2: 10-6 7-5 8-4 9-3 1-2


(see this Wikipedia article for more details)

Which player corresponds with which pairing number is determined before the tournament. Traditionally, this is just some kind of lottery, where each player is assigned a random number. It seems this was also the case for Sinquefield 2015:


  Pairing numbers will be drawn randomly at the Sinquefield Cup


For another Grand Chess Tour tournament, Norway Chess 2015, they had a blitz tournament the day before. The winner of that tournament could pick a number first. Because with an even number of players, you play an odd number of games,  the winner could pick a number, say 1, that would give him white in 5 games and black in only 4. The runner-up of the blitz tournament could pick next, and so on.