As I understand it in simplistic terms ('cos that's all I'm capable of!) a derate is a (semi-)permanent issue of engineering certification/set-up of an engine which reduces it's thrust capability to something below it's manufactured ability. (eg. 26k thrust derated to 24k thrust). This allows for extension of engine life, slightly different limitations perhaps, maybe different noise category etc etc etc.
A Flex take off is a specific thrust reduction for a specific take off, in addition to the pre-exisiting derate, to take advantage of the conditions (wx) that exist on the day at that airfield on that runway with that weight etc etc.