Cadance is technically the Queen or Empress of the Crystal Empire. But she will not be referred as so because Queens are associated with evil. Thanks Disney. Celestia and Luna are not Queens because with Queens there can only be one. Yes, Celestia was supposed to be called Queen Celestia, but that was before Luna was made as there was only one alicorn at the time. Cadance has royal blood in her as she is related to the first Queen of the Crystal Empire, Amore. Look it up on her wiki. I think when you become an alicorn not only are you as powerful as a quarter of the Equestria population but your DNA changes. Cadance is part of the Crystal Empire because she was born into it and Equestria Royal Family via adoption. So automatically Flurry is a princess of the Crystal Empire and Equestria.
Also you can be born into a royal title take Prince Blueblood, the distant nephew of both Celestia and Luna for example he didn't earn his royal title and so I guess he was born into his title. Flurry Heart has been mentioned as a Princess in merch.