I'm sorry to hear about your barn kitty.
I don't know if this will help you at all, but I the kitty probably never felt pain. The dogs probably attacked it pretty fast - unfortunately, I have seen a couple of dog on cat attacks before in my life, and it was over in mere seconds.
I also know this...massive trauma, such as bites, gun shot wounds, broken limbs, and muscle and tendon tears (which I know first hand about) it takes at least 10 minutes before any pain starts to seep through - one can feel something isn't right, but it's not pain.
This natures way of allowing an injured creature a chance to move and get away from things sometimes. I have read that people who are shot say it's like getting hit with a big pillow...they feel the blow but not pain. I have had friends break legs or arms and they say the same thing...there's a weird, almost numbness to it...and it takes some minutes before any real pain starts.
I have had the muscle torn from my calf bone and my Achilles tendon split and when it happened, I felt like someone hit my leg with a warm water balloon or something on that order...I felt a blow and warmth, but it was many minutes before I felt any pain.
So, I hope you can find a way to not dwell on the possibility that your kitty suffered much.
I know this probably offers very little comfort to you, but the chances are your kitty died very very fast and long before there was a chance of any pain setting in.
Stormy