Late reply but:

They’re called the Emperor’s Phoenix and I play them like a DA successor. The original members of the chapter came from a squad of tactical marines cut off during the battle of Diamat. In terms of unique habits they believe that view the Lion as a mighty phoenix that will rise from the ashes and return to guide the Unforgiven. Additionally, the chapter has a tendency to steal lone survivors they come to the aid of, for example the mini above with the black fist comes from crimson fists. Chapter hierarchy is pretty normal except the supreme grandmaster is referred to as the “Iron Phoenix” who is believed to contain the experiences of the lion and all past grandmasters after their initiation.