Could Iodine supplementation help cure dysbiosis/gut flora unbalance? Its a shot in the dark.
I would say it's a good possibility. Mineral deficiencies are more overlooked than vitamin deficiencies. If your going to supplement a diet, in the PHD Jaminet recommends not just iodine, but selenium and lithium (and other minerals and vitamins that you may or may not be getting from food already like sodium, and potassium).
I would pick up a copy of the Perfect Health Diet and consult it for ideas and dosages for your particular issues.