Perhaps their approach to avoiding detection was largely remaining in obscurity; for instance, the roadie, not the rock star. Whereas Flint was supposedly all sorts of famous/historically significant people.
Ever read Poul Anderson's
The Boat of a Million Years? I once considered pitching a Trek novel about Flint's life story, but then I read Anderson's novel and realized I'd just be duplicating what he'd already done. In Anderson's novel, there are multiple immortals, and they naturally try to keep from being discovered, but over the course of millennia, they still stumble across each other from time to time. Given enough chances, even improbable things become inevitable. So I have a hard time believing that in 6000 years of actively hoping to find another immortal, Flint never managed to discover even one of the numerous other immortals hiding around him.
and Data, Pelia, Vic Fontaine, Odo, Moriarty, and all the other people who might've lived another eight hundred years
Hmm... Not sure about Odo. We know that as one of the Hundred, he survived in a dormant, undeveloped state for centuries before he was discovered, and "Children of Time" established that he could live for at least 200 years beyond his then-current age. But that doesn't prove he could've made it 800 years.
Meanwhile, I've seen it pointed out that the tendency of fiction to assume that cybernetic/robotic characters are immortal doesn't make sense if you think about it, since in real life, the life expectancy of electronic devices is generally a whole lot shorter than the life expectancy of organic beings. Machines break down as easily as organisms do. Sure, a sufficiently advanced machine might be capable of self-repair, but so are living beings, and it doesn't make them immortal.
Okay, the Doctor proves that sentient holograms are potentially capable of lifespans on the order of a millennium -- but we also saw in
Voyager and in
Academy that sentient holograms are vulnerable to software breakdowns that can kill them, or at least require them to be reset to their initial state, which is effectively the same thing. So there's no guarantee that all holograms would have comparable lifespans. And I'm not sure anything's been established about the life expectancy of Soong-type androids. Yes, Data's head survived being buried in a cave for about 500 years, but it was inactive during that time, so that doesn't necessarily count. We did see some millennia-old androids in TOS, and Flint built Rayna to be immortal, but that wouldn't necessarily apply to every "species" of android. (In Roddenberry's
The Questor Tapes, which I like to believe took place in the Trek universe, the life expectancy of an android of Questor's "species" was about 200 years.)