Spirulina supplements is basically dried, packed ocean sea weed. It's literally also used as fish food. If you want to take the pills go for it, but the best way to get iodine is naturally in what you eat.
Instead of supplements, why not try something real? Some foods you could incorporate into your diet that are naturally high in iodine are ocean fish, actual seaweed and kelp,and salt. Take it easy on the salt though. You will actually GAIN weight because you'll start retaining water.
In my opinion..you shouldn't need pills and supplements to get and be healthy. You can find all of the things you need in what mother nature provides to you. (but that's it's own argument)