I am repairing a house with a flat concrete roof that has puddles of water in several places. The roof leaks on one side a lot and several small leaks in a couple of rooms. Everyone advises that I should contract someone to scrape and use 2 coats of acrylic and masterflex. But the puddles would remain. One contractor said I need a topping of cement w acrylic to level it out for drainage. That cost big bucks. What is the best solution even if it does cost more money.

While I am not a roofer, Every flat roof I have see has some puddles ( I've been on a number of commercial rooftops and seen many more from that vantage point. But puddles do not equal leaks. Voids in the waterproofing material equals leaks.

Leveling out may not be necessary (depending on how deep the puddles are), but it would provide an extra measure of safety from leaks.

If you have puddles several inches deep... I think you have a problem, if they are very shallow, then its probably normal. Those should evaporate fairly quick.