Hey there.
I play High Elves and am just getting into Lizardmen. The flame phoenix has a 2+ ward against flaming attacks. It is only toughness 5 w/ no armor saves. Poison does wonders against it. No, there is no way to prevent it from getting the chance to resurrect. He gets to roll every player turn, but it has an even better chance of being dead forever than coming back to life. Need a 6 to resurrect and a 1 or 2 to die. It get's better if you have an Anointed on top, though. I played a game with an anointed on a flame phoenix and all you have to do is kill the bird. Don't worry about the guy on top. If you kill the bird, the rider goes with it. Keep in mind that if it does come back, it comes with 2+D3 and so it isn't full life. Most people seem to like the frost phoenix more. I hope that helps.