I'd suggest that you not start them both at the same time, and because getting your thyroid hormones regulated is a lot more important, I'd start there. Are you just starting thyroid meds or have you been on them for a while? Do you have recent labs and reference ranges to post?
Once your thyroid hormones are raised, you should have an easier time losing weight and might very possibly not even need the phentermine.
There are no listed interactions with Phentermine and Synthroid however i would check with a pharmacist if you do not want to talk to your doctor.