This sounds like a fun assignment. Are you actually naming your own horse? I like your own suggestion of "Flash." You may want to check out some synonyms of various words that relate to "fast" or "speed." A few that come to mind are
- any word combined with "thunder" ("Thunderbolt," Thunderstruck," "Thunderclap").
You may want to consider giving it a historical or mythological name that relates to speed or power, such as "Mercury" (or "Mercurial") or "Apollo." I have also provided an interesting link that might be of help. It gives hundreds of possible names--specifically for horses.
There are probably any number of names that might fit the bill. My first thought is Lightning. There must be many more!
lightining, speedy, swift mofo, stallion, bullet legs
There are books and websites that list thousands of names of horses. Each source gives it own list which differ substantially from most other lists. Thus there are no universally recognized names for horses. Given below are links to three different websites listing names of horses. Last of these website lists more than 100 horse names associated with speed. I have chosen a few out of it that give the feeling of "fast"