No, you will not need to file an MO nonresident state income tax return unless you have rental income from renting out your vacation home in MO. Just owning an MO located vacation home does not require an MO state income tax filing.
You will still be able to claim a federal itemized deduction for any mortgage interest and property taxes on this MO vacation home.
You will only need to filing a KS resident state income tax return to report all income from all sources.