The yellow symbolizes goldenrod, Kentucky's state flower. The green, which has a slight blue tint, represents Kentucky being the Bluegrass State.
I wanted to symbolize "United We Stand" without just putting the motto on there, and I settled on a simple saltire. I view the two crossing lines as evoking unity. Even if it's quite the stretch, I think it looks great.
The checkered pattern comes from the checkered "finish" flag and represents the Kentucky Derby.