FYI: I am an Army veteran, but regardless of duty status, the pistol purchase process is the same for either of us. The states do not recognize service when purchasing a handgun. If you do not have a CCH permit, you may attain a pistol purchase permit from your local sheriff’s department by applying for the permit in person and then waiting several days for them to process it. You may then pick the permit up in person and pay the permit fee. The permit is relinquished to the FFL dealer upon purchasing the handgun. Without a CCH permit, this process is repeated for each handgun purchase.
Keep in mind this alone does not, nor does duty status, allow you to carry concealed in public. Though I highly recommend for qualified individuals to become familiar with the law regarding use of deadly force and to carry concealed whenever possible. We do not get to choose the time and place when a firearm is needed, though I understand it is a personal choice one must make.