Can you use a credit card to license a vehicle. If not, are there any office in the Kansas City area that do?

Yes you can but there is a service fee. The fee depends on the total cost of the transaction ranging from $1.25 to 2.15%

According to their website here https://dor.mo.gov/motorv/buying.php "Payment may be made by cash, personal check, cashier's check, money order, and credit or debit cards (Discover, American Express, VISA, and Master Card only). Personal checks must be made payable to the Missouri Department of Revenue. Personal checks must be preprinted with the check writer's name, address, bank code, and account number. The personal check must also include the following information regarding the check writer: - Driver's license or non-driver's license number; - Date of birth; and - Daytime phone number. The Missouri Department of Revenue may electronically resubmit checks returned for insufficient or uncollected funds."