I would have a competent gunsmith inspect your Kimber or send it to Kimber for repair. The gun is not safe if it double taps, this could cause a serious accident or even death. We do not need to give the anti-gunners any more excuses to say these and all guns are dangerous. As a Kimber owner I believe they are one of the best-made 45's and if mine ever fails to work properly I will definitely have it repaired.

My two cents worth.

Swede44mag

I too have had this happen and it took some doing to find the culprit. I have a Colt Officer's 1911 stainless with King's Gun Works' custom carry package.
On the third time shooting it it did a double-tap. I called everyone and had it looked at twice and the conclusion was that there was nothing wrong with the weapon. As it came about it did it again.
Ended up being all my fault. I had the trigger tightened lower than recommended and had an adjustable trigger as part of the package deal. I tightened the trigger screw too much and this caused the sear to release with the recoil.
Just my 2 cents of knowledge learned by screwing it up myself and not listening to the learned opinion of others.