6 Best Vines for Growing on Fences! When you're deciding to cover your chain link or other wire fences, look no further than these 6 beauties. These vines are the best for growing on fences, trellises, and lattice panels for privacy. Each is a fast growing perennial vine and all, except the evergreen ivy, provide gorgeous summer flowers that will attract butterflies, hummingbirds and bees. 1. Lonicera Scentsation - a well behaved honeysuckle variety that you can plant on fences, arbors, trellises.. 2. Madame Galen Trumpet Creeper - bright coral-red trumpet shaped flowers. 3. Bignonia...