Technically speaking, "flat" means constant gain across the frequency spectrum that you are interested in. PA amps are typically flat, and mixers tend to be when their EQ controls are centered.
Many (most?) bass amps are designed to have something other than flat response when their tone controls are centered. I don't know if there is an official term for this, but I call it "voicing." The reason for voiced amps is that they sound good, or at least, the designer of the amp wants it to sound good when you try it out with the knobs centered.
You can measure the voicing curve if you care what it looks like, using a real time analyzer (RTA). Going further, you can try to dial the EQ knobs on a voice amp until the curve is reasonably flat, as I have done as an academic exercise on one of my amps.
A few bass amps are known to be flat -- these tend to be favored by upright players.