Does flomax help kidney stones pass faster? Can it cause urine to burn and have brown spots? What happens if I stop taking it-will it not pass as fast

No. Flowmax will not help in passing a stone and women should not take it. Drink enough water daily so that your urine is mostly colorless. It will help in passing the stone and in preventing formation of new stones. Depending on the size and location of the stone, other interventions may be needed. .
Faster and no. Studies have shown that Flomax may help larger kidney stones (11-20mm) pass quicker (~ 20% faster at 4 weeks, accelerating as time goes on). Flomax itself is not known to cause urine to burn nor have brown spots; those symptoms may be due to complications of the kidney stone(s) themselves.