A card does not need to be in play/active at the timing it's triggering condition happened, merely in play/active in the window for its interrupt/reaction to be used. Therefore, Melisandre can react to herself entering play, much like Littlefinger and many other cards.
Melisandre's reaction only works when a character, location, or attachment is "marshaled" or an event is "played". It does NOT work when a character is "put into play" via Arianne, Reinforcements, etc.
Page 17 of the RRG: "Always resolve a triggering condition before initiating any reactions to that triggering condition." This means you play Seen in Flames, resolve it, and then trigger Melisandre.
- Melisandre can react to a cancelled Seen in Flames. RRG pg 7 "If the effects of an event card are canceled, the card itself is still considered to have been played, and it's costs remain paid."