There is no such thing (really) as "alliteration poems" -- or "alliteration poetry" -- at least not yet. But our language is forever evolving, and as writers experiment with new forms, who knows? While it does not officially exist today, it would simply be a poem with alliteration in it. Alliteration is the poetic or literary device of repeating consonant sounds. It pleases the ear. It's delightful word play. So why not use it?