I'll chime in here as well.
I'm sure others have touched on this.
First off, Flat Response refers to how the piece of equipment (amp, pre-amp, etc.) is designed to reproduce signals.
in other words, if the amp is designed to amplify signals from 20 hz to 20 Khz for example, then you definitely want that amp to have a absolutely flat response between 20 hz and 20 khz. a 20 hz signal should have a particular gain/response level from that amp. a 1 khz signal should have the exact gain/response level from that amp. A 20 khz signal should have the same gain/response level from that amp.
That is a flat response. The amp, pre-amp, etc. isn't adding of subtracting (missing) any information to the signal. it is not adding a signature of it's own.
However, many designers design to add additional bass or high frequency response to their equipment. This most definitely not a flat response.
I want my equipment to reproduce the signal exactly as it came in, flat from 20 hz (or lower) to 20 khz (or higher). Anything else is cheating and is adding a certain "sound" which is not accurate in the slightest.
Now, if the amp is designed in conjunction with a particular speaker for example, then there may be a need for some wave shaping circuitry to correct for the speaker's issues. many speakers require this wave shaping correction. However, it is typically in the crossover and not in the amp. my point is certain equipment is designed together to correct for issues from other equipment from the same manufacturer. This why as a system they sound great, but when used separately with other equipment, not so much.
thanks, enjoy