I took Glucosamine Chondrotin and Synthroid without any problems with interactions. In your position, I would ask the pharmacist selling the meds if both drugs would interfere with each other, just to be sure.
I only know you should be careful combining Glucosamine Chondroitin with Coumarins, because it may amplify the anticoagulant effect.
Have a good weekend,
You should check with your doctor or pharmacist to be sure. Please be aware that all vitamins/supplements should be taken at least 4 hours after levothyroxine.