Hippocampus erectus IS the breed. AKA Florida Seahorse or Lined Seahorse.
They'll breed easily enough. Rearing the young is a trick though. I've done it ... years and years ago.
Assuming they are correctly identified (as H. erectus) the babies will be benthic meaning they will hitch from birth.
I attempted with very limited success, Hippocampus reidi - they are a larger specie but have much smaller young, which are pelagic and don't hitch for the first few weeks.
But I digress...
Most seahorses are more than willing to reproduce in captivity but it takes some doing to rear the young in nursery vessels. I had the best luck using 1-gallon glass fish bowls with an airline siliconed to halfway down the side seam, and a gentle bubble that created a circulating current.
Google Kriesel aquarium.
As for flow, adult seahorses can tolerate a surprising amount of current, as Brandon mentioned. I had a male reidi that used to play in the current.
They do need some 'dead spots' with holdfasts where they can hitch and rest without being blown around.
Jenn