VA Flu Shot Walk-In Clinic at Galesburg VA Clinic. The walk-in clinic will be held on Tuesdays 1 to 3:30 p.m., Wednesdays 9 to 11:30 a.m., and Fridays 1 to 3:30 p.m. This event is solely for enrolled patients with the Iowa City VA Clinic. Veterans can enroll at 1-877-222-VETS. If you are unable to attend during the walk-in clinic times, you can call to schedule an appointment for your flu shot after October.