Your copter's motors will always act funny on the bench. This is because your KK2 is meant to manage motors in the air, not on a bench.
When bench testing your motors you look for 3 things.
1. They spin the right way. If you have any motors spinning the wrong way, your copter will flip on startup.
2. They don't "jitter". Jittery motors indicate a bad solder joint between the motor and the ESC. Don't throttle up! Shut down and fix the solder joints.
3. They all start at the same time. It doesn't matter on the bench if some motors seem to spin faster than others. On the bench that will most certainly happen if you have a working KK2 board. What absolutely MUST happen is that the motors start at the same time.
If you have all this working, these are the common causes of instaflip (copter flips or spins on launch).
1. Wires crossed. If you put the plug for ESC and motor 1 in the KK2's slot for motor 2 and the plug for ESC and motor 2 in the KK2s slot for motor 1, your copter will instaflip.
2. Reversed channels in your transmitter. Most transmitters have a setting to allow you to reverse a stick. If when you push right roll on your transmitter the copter gets left roll from your receiver, your copter will instaflip or spin. This one is really fun because if your copter is spinning left, you giving it right yaw is actually being received as left yaw making your copter spin even harder the more you work to counter the spin. In short, be SURE that when you give your copter a pitch up command, it gets a pitch up command not a pitch down command. Make adjustments in your transmitter. This will commonly cause either flipping or
spinning.
3. Backwards props. The writing on the prop faces up.... ALWAYS. You need two CW props and two CCW props. These need to be on the proper motors. If you put a CCW prop on a CW motor your copter will howl at you and you may instaflip.
4. Board not facing the right way. If you mount your KK2 upside down or backwards or 90* to either side it will flip.
These are the most common reasons for flipping copters. If this doesn't help, post video of the event and let us see it.
EDIT: it seems I was posting at the same time you were.
If your copter is spinning go into the KK2 diagnostics and look for a reversed transmitter channel.
Instructions are step 6 here.
Also, when you fly, POP your copter up about 1 meter off your launching surface and into "clean" air before you try to fly. The air between your copter and the ground is all swirly for the first few inches and not a stable place to fly.