It depends. Missouri does not have a true part-year return. Rather Missouri allows you to either file as a nonresident for the part of the year you lived in Missouri, or to file as a resident (full-year) and claim a credit for the amount of tax paid on the other state return.
Because you have this option for Missouri, the easiest way to file is probably to claim all of his Missouri income as nonresident income. By doing this, all of the Missouri income is taxed in Missouri first (as it should be by the way you describe the question).
If you file a joint Federal Return, Kansas also requires you to file a joint return. You may choose to file a joint resident return (which would claim a credit for the income he earned in Missouri on the Kansas return), or you may file a Kansas nonresident return as married filing joint.
Because of these laws, you might find it simpler to file both returns as nonresidents for 2018. I would certainly recommend filing Missouri as a nonresident return, and see whether a Kansas nonresident return or a married filing joint resident return (claiming a credit for taxes paid to Missouri on your spouse's income) provides a better result. Choose the option that has the lower tax liability.
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