How soon after a thyroid scan should you wait before an uptake scan?

One after the other. The exact scanning time after taking the capsule varies according to the isotope and protocol used. For i-123 and low i-131 the uptake and the scan is usually done at 24 hours. A thyroid probe directed to your neck measures the radioiodine uptake, this is follow by a gamma camera scan which makes an image of your thyroid gland based on the radioiodine distribution.
No time. If by scan you mean an ultrasound before a radioiodine uptake scan there is no need to wait. But why do you need both - one is usually sufficient, ask your thyroid doctor why both are being done.
Depends. Sometimes both are done at the same time (in the case of tc99m pertechnetate). Sometimes a radioiodine scan is done, which is followed by uptake measurements at 4 and 24 hours later. Ask your physician, .