I am a Florida concealed weapons permit class instructor and your information is correct. A DD214 is all prior military needs for the permit. You can get an application from the state's website.
In addition to a DD214, you will still need a passport photos (write your name and DOB on the back with a felt tip pen) and you'll need to get your fingerprints taken - a fingerprint card will be included with the application packet they send you.
If you live out of state your permit will say "Non Resident" on the top but its no big deal.
I used a DD-214 years ago for my permit and can tell you from my experience and many others as well the Florida permit is easy to get provided you file the application as prescribed.
Of course anyone else can still apply with the approved gun course documentation.