how often do cordeline flower

No, they don't die when they've flowered - enjoy and just trim the flowering stems off when they're over

They will flower once in any one year.

I've seen flowers in May 2 feet high and as much across on quite a small cordyline, very attractive.

What about branching. Do they tend to branch after flowering or only when tip tip gets frosted?

What do the flowers look like?

Have a look under C at the bottom of the page, Teddygirl, must be some pics there with Cordylines in flower. Not very impressive is my answer to your question!