Two relevant statutes regarding your request:
RS Mo 571.101 2. A certificate of qualification for a concealed carry endorsement issued pursuant to subsection 7 of this section shall be issued by the sheriff or his or her designee of the county or city in which the applicant resides, if the applicant:
(1) Is at least twenty-three years of age, is a citizen of the United States and either:
(a) Has assumed residency in this state; or
(b) Is a member of the armed forces stationed in Missouri, or the spouse of such member of the military;
So you qualify under (b)
And from RS Mo 571.101 (8) Submits a completed application for a certificate of qualification as defined in subsection 3 of this section;
(9) Submits an affidavit attesting that the applicant complies with the concealed carry safety training requirement pursuant to subsections 1 and 2 of section 571.111;
Which means you still have to take the training.
Qualification Requirements: RS Mo 571.111 1. An applicant for a concealed carry endorsement shall demonstrate knowledge of firearms safety training. This requirement shall be fully satisfied if the applicant for a concealed carry endorsement:
(1) Submits a photocopy of a certificate of firearms safety training course completion, as defined in subsection 2 of this section, signed by a qualified firearms safety instructor as defined in subsection 5 of this section; or
(2) Submits a photocopy of a certificate that shows the applicant completed a firearms safety course given by or under the supervision of any state, county, municipal, or federal law enforcement agency; or
(3) Is a qualified firearms safety instructor as defined in subsection 5 of this section; or
(4) Submits proof that the applicant currently holds any type of valid peace officer license issued under the requirements of chapter 590, RSMo; or
(5) Submits proof that the applicant is currently allowed to carry firearms in accordance with the certification requirements of section 217.710, RSMo; or
(6) Submits proof that the applicant is currently certified as any class of corrections officer by the Missouri department of corrections and has passed at least one eight-hour firearms training course, approved by the director of the Missouri department of corrections under the authority granted to him or her by section 217.105, RSMo, that includes instruction on the justifiable use of force as prescribed in chapter 563, RSMo.
Training Requirements: RS Mo 571.111 2. A certificate of firearms safety training course completion may be issued to any applicant by any qualified firearms safety instructor. On the certificate of course completion the qualified firearms safety instructor shall affirm that the individual receiving instruction has taken and passed a firearms safety course of at least eight hours in length taught by the instructor that included:
(1) Handgun safety in the classroom, at home, on the firing range and while carrying the firearm;
(2) A physical demonstration performed by the applicant that demonstrated his or her ability to safely load and unload a revolver and a semiautomatic pistol and demonstrated his or her marksmanship with both;
(3) The basic principles of marksmanship;
(4) Care and cleaning of concealable firearms;
(5) Safe storage of firearms at home;
(6) The requirements of this state for obtaining a certificate of qualification for a concealed carry endorsement from the sheriff of the individual's county of residence and a concealed carry endorsement issued by the department of revenue;
(7) The laws relating to firearms as prescribed in this chapter;
(8) The laws relating to the justifiable use of force as prescribed in chapter 563, RSMo;
(9) A live firing exercise of sufficient duration for each applicant to fire a handgun, from a standing position or its equivalent, a minimum of fifty rounds at a distance of seven yards from a B-27 silhouette target or an equivalent target;
(10) A live fire test administered to the applicant while the instructor was present of twenty rounds from a standing position or its equivalent at a distance from a B-27 silhouette target, or an equivalent target, of seven yards.
No where in the statues does it say that current or past military service qualifies an applicant for a CCW endorsement. Unfortunately that means the sheriff was wrong in telling shooter64738 this information.
One further note. If you receive a CCW endorsement while stationed in Missouri and you move to another post outside of Missouri, your Missouri CCW endorsement turns into a pumpkin.
I would suggest a Florida permit as it will work in Missouri and many other states.
Thank you for your service and may you have a blessed time while stationed here.