What if he just didn't know how. Like maybe Flint didn't know he was a Lanthanite say his parents were killed when he was a baby and he was adopted having absolutely no idea Lanthanites exist like every other Human up until the 23rd century. And perhaps he was able to update his identity so well that it never drew the suspicion of anyone of any subspecies.
Again, in 6000 years of actively looking -- nearly 100 typical human lifetimes -- it seems vanishingly improbable that he never got a hit even once. The protagonist of The Boat of a Million Years needed less than 3000 years to find another immortal. It's true that he needed modern communication technology to reach out and find them, but Flint (or whatever name he went by at the time) would have had access to that technology well before he left Earth and bought his own planet.
Besides, if Lanthanites' existence was already common knowledge prior to 2259, then as of "Requiem," Flint would have known of their existence for at least a decade, so why would he still have assumed his only hope of an immortal companion was to build an android?
For my money, if you send out an infant Changeling over two hundred years ago that also isn't expected to come home for another three hundred years then I'm gonna assume your natural lifespan is significantly longer than 500 years.
But "longer than 500" is not necessarily "at least 1000." Maybe it's just 700.