Electric Power Systems for a qudrocoper base on 30amp Speed Controller and NX-4008-620 - NX-4008-620kv Brushless motor
This is from an EE and not an RC perspective
 For actual in the fuield performance you want to ask RC people as it's really how well the products match their claims. 

People seem to like the flightmax OK. 20C = 20 x 4 = 80A.

BUT
Motor is rated at 180 Watt.
 Power = Watts = V x I
 or I = V/P
 As V drops P will drop and a claimed 180 W is probably at full charge.
 I'll assume that.

IF you want to run this at full power you need I = P/V = 180/11 =~ 16+ A.
 Four at full power ["Pull up! Pull UP !!!!!!!"] = 64A. The battery will be getting exercised at 64/80 = 80% of continuous rating but bearable IF they meet specs. 

But that's more than double the ESC continuous and still 64/40 = 160% of burst rate.
 The ESC is liable to burst when run above burst for more than about no time.

They recommend a 30A Esc for one motor so if you followed that you'd want about 120A ESC for 4 motors. I'm not aware of the technology so I don'y know if you get 1 channel per ESC or 4 in one unit. This is OK for one motor but not for 4. At a minimum you want about double the gross ESC capacity.

There should be relatively little in greatly boosting ESC power. Pretty much just bigger MOSFET(s) and a bigger heatsink.  16A at 10 milliohm Rdson =~ 2.5 Watts = modest heatsink. That's a very capable MOSFET. At say 50 milliohm on and 16A you get I^2 x R = 256 x 0.1 = 26 Watts = hot !!! Good FETs wanted. And leads, connections etc.

You could always limit it to what the ESC is happy with but power would be well down on what the 4 motors together are notionally capable of.