Hi Linda,
Breeding zinnias is a interesting hobby, and anyone could do it. Just saving seeds from your favorite zinnias would be easy to do, and that would constitute breeding, and actually could be quite effective. And if you happened to get a mutant, then saving seeds from it and/or crossing it with other favorite zinnias could get really interesting. Both of the mutants that are the basis for most of my current "exotic" zinnias came unexpectedly from commercial seed packages. I am currently growing some zinnias indoors, and this is one of my current interesting specimens.
It also has some of the "toothy" genes, but my "regular" toothies have three teeth at the end of each petal, while this one has a random number of teeth per petal, and the teeth can appear anywhere on the petal.
If you wanted to grow some unusual zinnias, the Whirligig strain that Stokes Seeds offers produces many unusual specimens in addition to the few multicolored specimens that they show. The reason that the Whirligigs have so much variation is that they were produced by an inter-species cross between Z. violacea (elegans) and Z. haageana (which contributes the multi-colored petals). The toothy trait that I have been selecting for also came from the Whirligigs.
I have been thinking about writing an article touting zinnia breeding as a fun hobby, but I have been so busy with my indoor zinnias and extending the size of my outdoor garden, that I don't seem to have time to write the article right now.
ZM