Getting rid of kudzu can be a challenge...but the best and clearest way is to kill it's root crown. It's difficult, BUT FAR less time consuming than herbicides and constant pruning.
Find a vine lead that leads to the ground. Start digging around it without cutting the vine. ONCE you've dug about a foot, you'll notice a large Woody piece, that's the root crown.
destroy it, cut EVERY woody root about a foot away from the crown in all directions. Once the root crown is harvested, destroy it by burning. While this takes a lot of hard work and muscle, it is far less time consuming than pruning, herbicides or chemicals.
With the crown destroyed, the vines will die and brown off, unfortunately that makes them a fire hazard, so start trimming the kudzu vines instantly away from any property