You may know that the ideal plant might not exist, in that it might not cover the fence at all times of the year, but I think your best bet would be a native (can usually take all weather conditions) that is also a vine. Here is a link to such plants for Oklahoma http://www.ehow.com/list_7190473_native-oklahoma-vining-plants.html Here's another site for best hedges for oklahoma, you will want something evergreen and hopefully native http://www.gardenguides.com/110375-hedges-plant-oklahoma.html

There are many wonderful vines - some perennial and some annual. For a well-behaved perennial I like sweet autumn clematis - it gets huge, covers itself in small white blooms and is fragrant. For an annual vine, you might like morning glories - there are so many pretty ones.

Sweet potato, morning glory, moonflower are all Ipomoea, so multiplying your vines with cuttings would work for any of these. With the extra wait since morning glory and moonflower are usually started from seeds, the sweet potato can give some quicker results because it is usually bought already growing. No reason to not have all 3 kinds if you like. Like any vine, their tendency will be to grow straight up and leave naked space below. If you give them a little guidance when you think about it, you can direct vines sideways for more coverage of the fence. Once they have some length, more than a few leaves, pinch off the growing tips to inspire side shoots to form. Occasionally pieces of vine may droop out toward the yard. Tuck those back into the fence, as low as they will go, to keep the coverage as solid as possible from top to bottom. The Clematis should be back next year, hopefully ready to do a little more growing but your disappointment this year is understandable. Everyone wants instant results! Bamboo - something like concrete or metal going deeply into the ground would be needed as a barrier to keep it from taking over your lawn. When you're tossing morning glory and/or moonflower (should you decide to use either,) there's no reason not to toss other flower seeds, something more to help cover the bottoms of the vines and fence. Just keep an eye at first to guide the vines up the fence instead of the other plants. If you put some landscape timbers or other kind of border separating other plants from lawn, it will be easy to keep tidy and trim against. If placed slightly sunk, the mower tires can run along the border to eliminate trimming an edge.

There are quite a number of wonderful perennial vines that grow in NH. (I am assuming that the NH in your user name indicates location, but if not these may not be good suggestions.) Some of the non-invasive honeysuckles include Trumpet honeysuckle (Lonicera sempervirens), European honeysuckle (L. periclymenum) and a couple of hybrids, Goldflame and Mandarin. Lonicera sempervirens 'Major Wheeler' last week There's a wide range of clematis available in sizes ranging from just a few feet to 15 feet or more, and they come in shades of purple, pink, reddish, and white. Clematis Mikelite late June Clematis Gravetye Beauty early July Clematis Prince Charles early July Clematis Venosa Violacea early July Clematis HF Young early June Clematis Ville de Lyon mid June The native pipevine (Aristolochia macrophylla) is mostly a foliage plant, with large heart-shaped leaves and pipe-shaped flowers tucked into the foliage. It provides food for one of the types of swallowtail butterflies. Another vine that can be grown for foliage is hops, Humulus lupulus, which is another really large plant. Besides the various green forms that provide the hops for brewing and their ornamental value, there is a gold-leafed form. There's a great photo of mature hops vines in this thread. Climbing Hydrangea will grow in part to full shade and has white flowers in June. It gets to 20' or more if untrimmed and needs a surface to climb such as a masonry wall or tree trunk so I don't think would work for your chain link. Virginia creeper (Parthenocissus quinquefolia) isn't great for a small garden as it is a large, vigorous plant, but is good for a woodland edge where it produces fruit for birds and has crimson fall foliage. It can be grown successfully on chain link fencing also. If you are interested in edible fruit, in addition to grapes, hardy kiwi vines produce clusters of grape-sized smooth fruit that taste just like tropical kiwis, but without the fuzzy coat. Both Kiwi and grapes will produce best with proper training. There are also various annual vines such as scarlet runner beans, sweet peas, and black-eyed Susan vines (Thunbergia) that you can plant between the perennial vines for a season or two while you wait for the perennial vines to get some size. Unless you have a really narrow area, you might also want to consider shrubs planted close enough to the fence so that some of the branches grow through the fence to help hide it. Hydrangea paniculata such as Limelight, Quickfire, or Vanilla Strawberry might work for this if the area is at least 7' wide.