how to up rank

For Silver tires ranking up should happen after 4-5 wins in a row. Ties can happen, but no losses. If a loss occurs, you start counting again. Also, games ending 16-14 or near to that will barely affect your rank since you barely got any points.

Each round is counted as a separate game. If your team wins the round - you take points from the opponents. The MVP takes the biggest part, and then they are handed according to the lowest guy in your team.
Ex: 2 teams: 4 Silver4 and one Silver2 against 5 Silver4
If first team wins a round, MVP takes most points, then Silver2 will take most points, since the odds were against him.

For ranks above Silver, the conclusion is that about 3 wins in a row should promote you, if you managed to get 1st or 2nd with a high number of MVPs.

I got promoted recently and here's how my last games went:
Loss; Win (16-7); Tie; Win (16-10); Win (16-8); Win (16-4); Promotion; Win (16-11) (matched only with guys from my new rank)

Only in one of those wins I wasn't 1st or 2nd. In the others I managed about 7 MVPs on average.

Kills/deaths don't matter, unless they lead to getting MVP.