I can help a bit with the difference between flex and a derate.
A derate rating is covered as an additional rating on the engine type datasheet. To use this rating, a full set of performance data must be included in the Flight Manual. Advantages include increased engine life, and the resulting reduced Vmc speeds are distinct advantage on some aircraft types.
Flex operations are covered by the existing engine rating and existing Flight Manual performance. The only thing that must be worked out is an acceptable method of determining the "flex" performance from the existing data, and this can be achieved in several ways, the most common (and probably most accurate without undue conservatism) is the "assumed temperature method", mentioned previously in this string.