If you want to see rate of uptake, you could load your cells with 6-methoxy-N-(3-sulfopropyl) quinolinium monohydrate (SPQ). I'm measuring NaI/NaNO3 exchange through chloride channels in human lung cell lines with this SPQ. It requires some expense to set up the microscope/imaging system, but I've read of it being done on a plate reader too.
Thank you for comments. ..some answers to queries. Breast Cancer cells stimulated with retinoic acid are supposed to take up NaI. I will check on the Anal Biochem Ref-. I never knew about the SPQ approach-can you provide a Ref ?