Amazing-Man Comics was published by Centaur Publications from 1938-1942. The primary character, Amazing-Man was created by Bill Everett who would later go on and create the Sub-Mariner. Centaur Publications went out of business in 1942. By the 1990s the entire Centaur catalogue entered into the public domain. The series ran for 21 issues. The series started with issue #5. I couldn’t tell you why, but it’s probably because it recycled the numbering from a previous title. This was not an uncommon practice among comic book companies during this period.
In 1992, Malibu Comics tried to revive the Centaur line of heroes. It didn’t go so well and the line eventually ended. Incidentally enough, Malibu Comics was later purchased by Marvel Comics.
Anyway, Amazing-Man was later picked up and used by Marvel comics, first in The Immortal Iron Fist: Orson Randall and the Green Mist of Death. He later went on to appear in issues of Secret Avengers, and The Defenders as the Prince of Orphans.
Are these stories considered part of Marvel Continuity? Well the only entry on the character can be found in the Official Handbook of the Marvel Universe A-Z Update #5, that story glosses over his origins in a vague way possible. It cannot be said with any certainty that. Confusing matters further is the fact that Malibu Comics made an earlier attempt to revive Centaur’s characters in the 1990s. The Centaur revival was a flop, but Malibu (and all it’s original materials) were bought by Marvel Comics. Per the Official Handbook of the Marvel Universe A-Z #2 the Malibu/Centaur universe exists as part of the Marvel Multiverse and is designated Earth-1136. So at the very least, those stories are considered canonical to that universe.
As Centaur Publications have entered into the public domain you can legally download every issue of Amazing-Man Comics for free. They are available on he Digital Comic Museum.