What is a flat rated engine?
Yes, a flat rated engine (my familiarity is with gas turbines, but the concept may apply to other engine types), is an engine for which the control system is designed to achieve the same level of thrust (hence the "flat" term), up to a certain OAT, then for higher ambient temperatures, the level of thrust decreases as a function of OAT, normally in a pretty linear fashion. This control system operation gives identical performance over the flat portion of the OAT range even while the engine degrades (until it degrades to the point it hits the EGT limit), making the plane performance predictable. But for higher OATs, it stops the EGT continuing to increase. The temperature at which the thrust starts to decrease is typically 25 or 30 deg C, and can be found in the EASA or FAA engine type certificates (e.g. see section 6 of this EASA one for the CFM56-5). See the graph from this CFM56 document below. So, your understanding was correct.