Having had an underactive thyroid for over 10 years now I would not recommend having Kelp supliments because of the iodine.
This is the information I found on the net which seems to agree.
Iodine
It is well documented that a diet low in iodine is associated with hypothyroidism or under-active thyroid. The best supply of iodine is from sea salt and seaweed. In Japan, for instance, the daily intake of iodine from seaweeds is estimated to average 3mg per day and thyroid disorders are known to be extremely rare. However do NOT take ANY iodine supplements without first consulting your doctor because excessive amounts of iodine can also lead to hypothyroidism.
I try to stear clear of anything which has iodine in it including some cough medication.