Why the cost of oil? Cost is a f(supply, demand). Demand in the US, as you say, is flat. Demand in the rest of the world: maybe not so flat. Supply out of existing fields is inexorably going down. Supply out of new fields is increasingly more expensive. Much of the supply comes out of places and countries that don't like the US and would rather sell oil to other customers, or just leave the oil in the ground for now.
Also, increased US money supply increasingly winds up in the hands of counties we import from. They buy oil too, and their money competes with our money. Increasingly they get the oil and we pay higher prices for what's left.