Thommy H-H
Hero
This is explcitly the stance taken in Eberron: Forge of the Artificer. The Dragonmark feats aren't gated by species or anything else. That's obviously what makes them interesting as ideas for something equivalent in other settings. In my homebrew games I've had Aberrant Dragonmarks show up, albeit as a result of arcane bioengineering as part of a half-dragon-warlord-seeking-draconic-apotheosis thing, but for some reason it's actually never occured to me to use the other Dragonmarks, even though I have a whole nation transforming into dragonborn and dragon moons showing up in the sky and just a big mess of dragon hyphen type stuff happening.For my personal version of Eberron, I split the difference. The majority of Dragonmarks are passed on via familial/"genetic" lines, but there are enough spontaneous marks that a PC of a different-than-expected race won't be some massively weird outlier. Most Houses are between 90-95% made up of the "standard" race.
I did just try seeing if I could map the Dragonmarks onto the canonical dragons, but it's not an easy fit (normally you can just about beat that kind of setting detail into shape!). Obviously Storm is blue, but beyond that you kind of have to stretch a little bit, especially because there aren't any 'evil' Dragonmarks (except Aberrant).