Whilst you are interacting with patients about their illness you are in a good position to link to any services that may be appropriate to them. In this instance entering into a conversation about your flu service (if you offer one) would be appropriate.
When offering this service to patients you need to ensure you are doing this in the best interest of the patient to deliver excellent customer service.
You may need to explain the benefits and features of having the vaccine and establish if they are entitled to it free on the NHS or if they would need to pay for this as a private service.
Find out from your pharmacist the details about your flu service, the booking process you should follow and the costs for the service.