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Hybridized figs may not yield edible fruit, and the problem with ivy is finding two different varieties to cross. Only plants of the same species will produce fertile offspring.

You'll need to fertilize the female flower, collect the seeds, and nurture them. The links below, although not specific to vining plants, offer the basics of hybridizing.

http://www.rhododendron.org/v50n1p36.htm

http://forums.gardenweb.com/forums/hybrid/