Starch is used as an antidote to iodine "poisoning", and the action of the starch will sequester the ioDINE(aka I2, molecular iodine, triiodide ion). I don't know that the starch complex keeps the I2 sequestered and then absorption takes place in the intestines or not. So, if you take starch with iodine(and a form of starch previously discussed on this forum is potato starch), then you may not be getting the benefits of I2. If you are concerned about discomfort from lugol's, then I suggest that you use iodoral instead:
"Starch itself contains two components, the branched amylopectin and the unbranched, linear amylose consisting exclusively of α(1-4)-linked glucoses. Only the latter produces the blue complex with iodine which, therefore, is more adequately described as amylose-iodine. In this complex, amylose forms a helical structure of 8.0 Å pitch with an outer diameter of 13.0 Å, a 5 Å wide central cavity and 6 glucoses per turn. The cavity provides enough space to accommodate iodine atoms. They line up to produce a linear polyiodide chain with an average I-I separation of 3.1 Å, a characteristic distance also observed in other iodine complexes which are deeply colored due to the presence of polyiodide chains."
Essentially, the cavities formed by the starch helices have enough room to sequester the iodine (or more correctly, the triiodide ion), which reduce its presence in the free form. Less free iodine, reduced toxicity!
The second reference below includes a structure. Hope that helped!