What is flat impedance?

The impedance curve of a speaker refers to its impedence in relation to frequency (to plot, put impedence in ohms on the Y axis, frequency in hertz on the X axis). When you're talking about AC waveforms, the "Resistance" is referred to as impedance.
The speaker will have a different impedance with a 50hz signal applied as opposed to a 10Khz signal.
To tell if a speaker has a flat response, you'd need to look at the impedance curve. Stereophile.com has loudspeaker reviews, and has the curves on the "Measurements" page.
Generally speaking, the flatter the curve, the easier it is for an amplifier to drive the speaker. Also generally speaking, it's easier for an amp to drive an 8 ohm speaker as opposed to a 4 ohm speaker.
For example - My Magnepan speakers are 4 ohm speakers, but since the response is very flat they are considered easy for an amplifier to drive (although they are rather inefficient...)

The impedance curve, as it relates to driveability, also has to do with impedance phase angle vs. frequency (greater phase angle magnitude = a more "reactive" or tougher load, lower phase angle magnitude = a more "resistive" or milder load). In combination with the impedance magnitude vs. frequency and the sensitivity these describe how difficult a speaker load is for an amp to drive (i.e., how much current the speakers demand and at what frequencies). It's the impedance magnitude curve that will give some idea about how much frequency response modification will result from using an amplifier with high source impedance, such as some tube amps. But the important thing to take away from this is that these measurements all vary with frequency, and cannot be accurately described by the "nominal" rated impedances that manufacturers spec their speakers at.

Unfortunately, these "complex" speaker measurements aren't something most folks are equipped to determine for themselves at home, so other than auditioning a given speaker with a given amp and judging the sonic results, you must rely on manufacturer's or reviewer's detailed measurements to get an informative idea about how easy or hard a speaker should be to drive and how it might modify the response of a partnering amp. (In the real world, driveability is also affected by factors ranging from types and sizes of drivers and cabinets, to room size, to preferred program material and listening levels, and the speaker cables used have their influence as well.) John Atkinson's commentary on his test measurements of loudspeakers in Stereophile is very educational about this subject, but note that the simple reference "dummy" speaker load he uses to calculate response modification in his amplifier measurements (based on their output impedance) shouldn't be taken as anything like generally representative of all speakers, as his own measurements show.

Thanks All who responded,this subject is a lot more involved than I realized.
Peace

Who makes some of the easiest speakers to drive?

I'm just curious to see what you all are using with tubes.
I'm looking for a list of speakers to audition that will be kind to my amp.