The phoenix is a monster from Greek myth which, after living alone in the desert for half a millennium, consumed itself in fire and rose again from the ashes. It is shown as a demi-bird issuant from flames. Medieval emblazons always gave it a prominent crest atop its head, as in the illustration (taken from the standard of Ralph Verney of Pendeley, c.1510 [Walden 138; cf. Bromley & Child 184]); modern emblazons often show it as simply a demi-eagle.
The phoenix is displayed by default: even when blazoned “rising from flames”, as it often is, its posture is displayed, not the heraldic posture of rising. The flames need not be blazoned (unless their tincture must be distinguished); without flames, the monster wouldn’t be a phoenix. See also firebird.
The Baron of the Sacred Stone bears: Vert, a double-headed phoenix and in chief a laurel wreath argent.
Sarah Davies of Monmouth bears: Or, three phoenixes sable.
Eiríkr Mjoksiglandi Sigurðarson bears: Per chevron gules and Or, three phoenixes counterchanged.