Parking in the market square is free for two hours, the entrance is currently only accessible from 3rd St. Parking on the outer lots is $1/hour, Monday-Friday from 7:00am to 6:00pm, you may use cash or card at the kiosks in the lot.
There is a section of free parking at the City Market, otherwise it's $1 per hour Monday - Friday 7am - 6pm in the pay sections. Weekend and weekdays after 6pm parking in most sections is free. This is from thecitymarketkc.org/parking/
I'm not sure unfortunately but weekends are free.
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