No. Ordering on someone else's behalf can be treated as making a medical decision for them, which sits outside your non-clinical role. Your clients request products themselves and complete their own medical intake, and an independent clinician prescribes only when it's appropriate.
This is by design, not red tape. Keeping the request in the client's hands is part of what keeps the prescribing decision with the licensed clinician, where it belongs, and keeps you in your non-clinical lane.
What you can do is educate your clients on the products that fit their goals. The request itself has to come from them.