Which Camera would be better for Continuous Flash Capturing?

I need a camera that can do a Continuous Shooting with a External Flash. I wanna capture several pictures quick and right after the other. My choices are:

Canon Rebel T2i
Canon T3
Canon Rebel T3i
Nikon D3100
Pentax K-r
Canon EOS 60D

Flash units that will do instant re-charge are very expensive… Do you have such a unit? If not I suggest you do some looking around the web because I suspect the flash unit will cost you more than the camera.

All these cameras do burst, of course, but not with the built in.

You need to be more specific! How many shots do you need to take and how quickly? Most of the cameras you list are capable of at least 3fps burst, but may slow down after taking several shots. They would need to be hooked up to some type of external flash, most probably mains powered, and has been previously stated this would probably cost more than the camera.

Speed wise when it comes to burst shots with basic equipment the king of the hill is Sony's SLT-A77. Teamed up with their HVL-58AM set to 1/16 or 1/32 it will burst shoot 12 shots in one second, before slowing down to just 1 or 2 per second (until the flash unit powers down due to overheating). The SLT-A65 can manage 10FPS under the same conditions at around 2/3's the price. *This speed of strobing could cause epileptic seizures to susceptible people.

Try here, here are many cameras of latest models in minimum price. Hope it will be helpful for you. Read their specification and compare if they match to your requirement. All you need to think about your requirement.

The T3i with a 580EX II (and an external power supply or battery pack) can do this. Probably. With any flash unit under TTl control, it will depend greatly on how much power the flash has to put out for each shot. If it has to fire at full power each time, you are only going to get maybe 2 shots per second, and around 10-12 shots before the flash shuts down due to heat.

Under manual control, you can get more shots faster, but you still have a limited number of shots before the unit shuts down due to heat.

If you want high speed flash with high power over any period of time, you will need AC powered strobes or monolights, and even then not at full power.

Give a little more detail on exactly what you are trying to achieve, and you will get better answers.