You are correct that Missouri does not tax military income.
Make sure when doing the Federal return that the Personal information section you have that you are Military and also when entering the W-2 in the Wages and Income section. Also make sure you answer questions after entering it that the income is Military. When doing this in the Federal section the deduction on the Missouri should automatically take place. But review the State return to make sure.
Military Income Deduction --
http://dor.mo.gov/personal/whatsnew/Senate Bill 814 (Section 143.174, RSMo) provides a deduction for military income earned as a member of the active duty component of the Armed Forces of the United States. The income must be included in the federal adjusted gross income and not previously taken as a deduction. This deduction can be claimed on line 19 of the 2016 Missouri Individual Income Tax Return (Form MO-1040). When submitting your return, include a copy of your Leave and Earnings Statement and any other official document, such as your Military Orders, which validates how long you were in active duty status and the amount you earned in active duty status. Failure to attach the requested documentation may result in the disallowance of this deduction.
