Very, very rarely. Most flowering plant breeders who intentionally produce triploids do so because they don't tend to set seed so they'll keep on blooming, but there's the occasinal rare instance where cells in meiosis don't divide in either the anthers or ovularies and allow a self.

It's been years since I was studying the breeding of various orchids. But, triploids do sometimes breed. But, mostly they are used as seed parents. In triploids the chances of being female fertile are higher than for being male fertile. So, self pollination is much less likely than for use in crosses with diploids or tetraploids. One example is the famous SLC called Jewel Box 'Sheherizade', which is a triploid. Many cymbidiums are triploids. They tend to make great flowering plants but are rarely used in breeding. Many that were not used were later found to be weakly fertile and subsequently were used to make some outstanding cyms. One example that I still remember is C. Hunters Point 'Sunset'. Some of the tetraploid x diploid cymbidiums produced many awarded clones but were little used in later breeding. A good example of this type of cross is C. San Francisco, which yielded many awarded triploids.