If its a wood fence, don't do it. Almost any flowering perennial vine will pull it down. If its chain link, still be careful. Not perennial, but runner beans are lovely, easily grown, won't pull your fence down, give you lots of food, and will attract butterflies and hummingbirds. Some of them will self sow.
Many flowering bushes can be propagated from cuttings. Lilacs for example. Get one or two flowering bushes that you like and start propagating cuttings to fill in the rest of the fence line. Runner beans or climbing nasturtiums (SUPER easy to grow) or cardinal climber etc in the meantime.
