Everyone else on the planet is pulling kudzu as fast as they can to keep it from smothering all other life forms, and you want to plant it!? I get it that you want your yard to be jungly looking. It is counter-intuitive when you live in Arizona. You might want to consider moving somewhere moister if you really want to live in a jungle... Cincinnati would probably suit you just fine!
But kudzu is so nasty. Think about planting grape vines and making wine. Grow hops and make homebrew beer (common hop is a pretty flowering vine and is a native plant in your area, so should be easy to grow).
Think about clematis, winding mariposa lily, butterfly pea, vine milkweed, perennial sweetpea, arizona honeysuckle vine, climbing snapdragon, woodbine, all nice native flowering vines...