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So, I have gotten several shinies throughout playing my Moon game, and for fun checked all of their Hidden Powers cause why not? I was suprised to see that 4 of them had Dragon HP and 2 of them had Psychic HP. Is this some crazy coincidence, or is Dragon HP very common?

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By any chance, were you also hunting for perfect IVs?
Uh, no? Is there a relation? I mean, I randomly got each of these shinies, two were SOSed, one was bred (but in the 16th egg, not enough to IV hunt), one was an event and two were random encounters.

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Hidden power is determined by IVs. Psychic and dragon hidden powers both require several odd IVs. Because all perfect IVs are odd, the shinies from SOS battles and events are more likely to have psychic and dragon hidden powers. There are other hidden powers that require relatively many odd IVs, such as ice and dark, so this is still a coincidence. It's just not a crazy one.

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