Only very few types of drug coverage (such as VA or TRICARE coverage) work together with a Medicare Part D plan - and, in general, drug store discount cards or private drug discount plans usually cannot be combined with a Medicare Part D prescription drug plan to provide extra cost-savings.
As noted by the Centers for Medicare and Medicaid Services (CMS):
"Drug stores issuing the discount card will determine what type of discount will be applied to the drug. Generally, drug store discount cards provide a discount on the retail price of the drug not otherwise covered by a patient's insurance. Since people with Medicare will be receiving coverage for prescription drugs, further discounts may not apply."