You can get it to spawn next to your base because of the following: It always respawns at it's last location, so if the heatwave ends while you are following it you will know where it is for the next heatwave. It also chases you when you eat flowers... hint hint
Find a phenix during a heatwave and follow it until it ends. The phenix will turn into ashes and land on the ground but will spawn right back at the same exact spot during the next heatwave. Build a trap 6 blocks high so I can't glitch out and you have yourself a trapped phenix to tame:)
Two-person tame. Get one of you to eat a rare flower consistently, like have at least 30. Once you've successfully located a Phoenix (they're smaller than you might think), both people must be on a high-health fire wyvern. Then, whoever is the designated rare flower bait, start on your duty. As the Phoenix attacks, both must flame breath the Phoenix. IT tames in no time at all. Just remember to keep on those rare flowers, or the Phoenix will de-aggro and speed away from you.