It seems that we would play KY twice just once every three years. There's 12 teams besides UT and Vandy. We play four of them twice every year, so it takes three years to play everyone twice in a single season.
Sounds like in two of the three years, we'll get three from the former East twice (counting Vandy) and two from the former West. In the other year, we'll get two from the former East (counting Vandy) and three from the former West.
Possible sets of opponents to play twice, using alphabetical order:
2013: Vandy, Florida, Georgia, Alabama, Arky
2014: Vandy, KY, Missouri, Auburn, LSU
2015: Vandy, USC, Ole Miss, MSU, TAMU
That's how I interpreted it.