Hi,
Thyroxine is to be taken early morning on empty stomach. Half hour you aren't supposed to eat anything.
Vitamins r basically of two types, fast and water soluble. Gluten didn't really interfere or help in absorption.
You can take the vitamin and calcium supplements in the afternoon post lunch.
Personally, i advice you to take food rich in vitamins and minerals i.e vegetables and fruits than going for supplements.

Hello Nella, Thank you for writing HCM. I understand that you are on thyroxin which is a synthetic form of T4, an inactive thyroid hormone that is produced by the thyroid gland when adequate iodine is in the diet (although autoimmune factors can play a role as well). You should take your synthroid first thin in the am with water one hour before food. Soy products should be avoided. Goitrogens may also interfere with synthroid. Adequate selenium needs to be present for the conversion of T4 to the active form T3. As far as correcting your absorption issues the best way to do that is to stay away from gluten that causes inflammation and malabsorption. Calcium carbonate should be taken with meals, calcium citrate can be taken with or without meals with regards to absorption. Magnesium is best absorbed with an acidic juice. Vitamin D can be taken without regard for food. Minerals such as calcium or magnesium need to be taken four hours after the thyroxine in the morning. A full glass of water should be taken with your supplements. Regards, Kathryn Shattler, MS,RDN