Depends on your deck, really.
Purifying fire can be used to clean up your hand effectively. Note that it can't be discarded by the flare attack. There are also multiple ways to "poison" opponent's hand with card like
Cleansing. Last, but not least are the direct discard cards like
Intrigue or
Ambush.
If you want to discuss a strategy how to deal with Phoenix, you are free to open a card specific thread in the cards section of the forum.
Also note the following:
- when summoning via Phoenix feather you have time to prepare (he doesn't have enough Burning cards for rebirth)
- Rebirth is always processed before the Flare attack, so you just need to keep either his Burning cards low, or his resources low (Phoenix isn't cheap), or just discard the Phoenix (it costs you resources, but your opponent has already spend resources and time)