Can I use tincture of iodine to supplement my iodine intake? It differs from Lugol's in what it has sodium iodide instead of potassium iodide. Both have elemental iodine in them. Sodium iodide also treats deficiencies. But why Lugol's is recommended for supplementing and tincture is not.
Molecular iodine is not something you want to supplement with, iodide or iodate are. Molecular iodine is toxic, that's why it's used as an antiseptic.
Better yet, if you're going to supplement iodine, "supplement" with foods rich in iodine.
If you need iodine, the best place would be some kind of seaweed (look in Japanese section of supermarket or health store). But there are other places to get it, like iodized sea salt if you include salt in your Paleo diet. There are kelp "drops" in health stores but I honestly don't know how effective they are, and emergency iodine pills you can generally only buy online for protection from nuclear fallout (not to be used daily). In a survival situation, you might ingest small amounts of the toxic form of iodine and it might be used by your body after being detoxified at a slight expense to your liver which does heal. That's why it's important to follow label directions carefully.
So the easiest way is to wrap up some paleo snacks in nori sheets.