How much sea kelp can a person take without overdosing?

Dubious supplement. Sea kelp is a widely-promoted "natural" source of iodine; unless you live in a part of the world where iodized salt is unavailable, there's no reason to supplement. The kelp concentrates environmental arsenic heavily but there's no reports of anybody becoming acutely ill. Taking lots of iodine can unmask hyperthyroidism. Talk with your physician.