I've seen way too many "buff phoenix" threads that have people saying that his ult needs buffs or the healing rate on fire is too little when they're actually very strong and are his best utilities as a character. The two things that need changes are his flash and wall, one change each.

His flash should be 2/3 secs (Breach/Skye duration) long to make up for how predictable they are. There is no reason why a Yoru flash, which can come from unreadable angles ALSO has a longer time flashed. EVERY flash bests him in one way or another, there needs to be an edge that makes people want to pick Phoenix's flash for a certain reason. If he can't have the ability to throw flashes from different angles, give him longer durations.

His wall has the same problem Viper had where people just don't respect it at all without the threat of a flash. Walking through the fire should blind them for a second or even less. Enough for it to be an unfavorable risk to push instead of a mild inconvenience. Done, the character can now compete with Jett as a controller/duelist hybrid while still having significant flaws IMO.