A tattoo of a flying pig is most likely a depiction of the popular idiom that compares the probability of a certain outcome coming to reality to the very improbable circumstance of a pig being able to fly. This may be to commemorate an unlikely event that has already occurred, or serve as a reminder some goals are unlikely to be accomplished, and it is wisest not to pursue them.
A person might choose an image of a pig in flight as a tattoo to symbolize a highly unlikely achievement that he has indeed accomplished, as a sort of testament to that very accomplishment. For example, a person in a mobility-impairing accident may have been told that he will walk again "when pigs fly," and upon being able to walk again, desires to get a tattoo to commemorate the event.
Besides these more idiomatic situations in selecting a tattoo of a flying pig, a person might do so as a reference to the city of Cincinnati, which has a past in the pig trade and where a flying pig is an unofficial symbol of the city.
Similar idioms that describe the unlikeliness of an event to occur are "when hell freezes over," and "not in a month of Sundays."