Unlike Deathflare, brand of purgatory has no note that using it ends Firebird trance. You need a buff tho from casting fire ruin 3.

So you can go ruin 3 deathflare, ruin 3 deathflare rinse and repeat until FB trance done.

Or am I missing something?

I guess it is technically upgraded outburt but looks more or less like fire deathflare to me.