As already stated, there is no such thing as a "flat" monitor. If you find a set with a flat response chart, there are a couple conditions to that. First, they've used some amount of averaging, there will be very narrow peaks and dips that are way outside of +-3dB if you chart detailed enough. Second, that measurement is done without room interaction.
Also as mentioned, your room will have way more influence than the speakers themselves. You'll be better off spending money on difusers, bass traps and other acoustic treatments. Bass traps are the most useful, because the long wavelengths of bass and standing waves in your room are by far the biggest problems.
EQ is not a good method for correcting these things. Many of the issues are time based, such as early reflections or woofer / tweeter phase and delay issues. There is no EQ in the world that will compensate for that. Standing waves in low frequencies are also simply way too large of a variance to compensate with EQ, and to top it off the EQ would only be valid at the exact position you've placed your measurement mic.
Also, wishing for a full 20-20kHz of flat response is really over the top. Producing output down to 20 requires some huge amounts of air movement. A full range monitor will never get there, unless you're into $10,000 soffit systems and are willing to put that much or more into your room acoustics. If you're looking at full range monitors, you'll do OK with at least an 8" woofer and you'll realistically get down to 40 or 50Hz in your room. If you need that last octave, you'll have to go with a subwoofer or use a spectrum analyzer.
Ultimately it comes down to learning your monitors by listening to well produced material that you know very well how it should sound. Move your mixes to as many systems as possible, headphones, home theaters, cars, crappy boom boxes, iPod docks... everything you can try. Listen to your mixes over and over again, and when you hear something, change it and start over.
Lather, rinse, repeat.