MO can tax all the income you earn by working in MO, regardless of whether or not you are an MO resident. So if and your spouse both worked all year in MO, 100% of your income would be taxable by MO - including the portion you earned after moving to KS.
The income you earned after moving to KS would also be taxable by KS, but you'd be able to take a credit on your KS return for the taxes paid to MO on that portion of your income. This prevents double taxation.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
