it's assumed that iodine/iodide/whatever (i'm no chemist and simply trust if it's a reef supplement it must be the right form), helps 'soft fleshy' corals like leathers, zoos and lps. it's also said to help detoxify excess oxygen that is produced within the zooxanthellae within coral when in really bright light. they say it is skimmed out by big skimmers.
i don't think anyone has really proved it, and some experts say there's plenty of iodine in the salt mix and food so that there's no reason to supplement it. however, i do notice my tank looks better when i do dose it, so i like it. too much and i get brown dust algae (which most people call diatoms).
i use the kent stuff (not the newer tech formula but the other 'red label' one). apparently it is time released. i generally like seachem stuff better than kent, and warner best of all. i use the kent just because i have a big jug that i've had forever. i tried lugol's a while back but didn't notice anything either way out of it. it's a much more potent 'raw' form that you add just a few drops of at a time.
if the leather is rotting from the base, i don't think it's flow. leathers can really take a beating, worst i'd expect from too much flow is it'd stay shriveled up. it sounds like it just didn't take to your tank. i'd cut any rot off with a razor blade and hope it settles down. keep up with carbon and skimming.