After walking my right buttock hurts after a 2 mile brisk walk.

Half pigeon!: Agree with the other doctor's answer that stretching beforehand can be helpful. I would add stretching afterward as well. Regardless of when getting into "half-pigeon" pose (yoga) will give you a perfect stretch of that area. Making sure you have excellent shoes on your walk is imperative as well. If that doesn't work, be seen to check leg lengths, need for insoles or gait training, etc.

Buttuck pain : The pattern of your pain brings to mind several things. Arthritis of the sacroiliac joint, problems with a nerve from the lower back, inflammatory muscle issues or problems with your circulation. So to help the pain I suggest speaking to your doctor to understand the cause.