Well, first, before I realised I could do it, I downloaded the newest version of Kies because I got all kinds of errors when i did a kies software update from the older version. I had to uninstall it from my computer and install the newest one. I got it from here:
btw, I did all of this with the phone completely stock - restored to unrooted KH7, then did OTA KK6 upgrade. NOt sure if it would matter since you will start in download mode anyway.
after completely finishing installing kies (and it took a while) i shut it down and then made sure the computer detected the phone in different modes (usb debugging on And off, and in download mode.) it will install the drivers when you connect it in each mode.
now, WITHOUT the phone connected, start the new Kies and went to the tools menu. Chose Firmware Upgrade and Initialization. It asked for the serial number and model number that I got from the sticker under the battery. Now, put the phone in download mode (either with a jig, or holding vol. up + vol down and inserting usb cable).
After you enter the serial number and model number it should say that the latest recovery version is the LE5 (the new firmware). Now, just leave the phone connected and keep clicking through with OK. It should download the firmware, and when it is finished downloading you will see the blue bar moving across the phone when it is installing.
Hope it works for you.
As with everything else on here, I'm not responsible if you damage your phone.
I dont think I left anything out but if you get to something that looks like I forgot to mention, ask and I'll probably remember.
AT&T Samsung Galaxy S3 i747
Current Rom: Stock 4.4.2
AT&T Samsung Galaxy S2 i777
Current ROM: ShoStock3 Jelly Bean by Shoman94
AT&T Samsung Galaxy S i897
Current ROM: Stock GB (given to my Dad)
Barnes and Noble Nook HD+ (Stock; all of my flashing is done on my phones.)