I have a KitchenAid KUDS01IJ Dishwasher. The Rinse Only light is blinking and cannot be turned off or switched to another setting. Multiple presses of the Cancel/Drain button will sometimes have the display show '2' or '---'. A few minutes later the display goes blank and the Rinse Only light starts to blink.

SOURCE: Kenmore Ultra Wash Dishwasher - Blinking Quick Rinse Light

My guess is that the foil that the buttons are mounted to is defective.  The control module "reads" the buttons that are pushed by the fact that the resistance between two pins on the circuitboard becomes zero ie. your pushing the button shorts out two pins.  the foil could have moistire damage or the resiistance of the tracks could be too high.  Solution for both would be to replace the control panel button foil.

SOURCE: Blinking "rinse only" & "cancel drain" indicator lights

have you unpluged for 5-10mins? check manual for fault codes..genrally in rear. Sorta sounds like a drain problem...maybe...very common.

SOURCE: Kitchenaid Dishwasher Control Panel lights - some don't light up

about the only thing to try would be to remove the inner door panel to get to the control bd then you will see a mylar ribbon looks like a fat piece of scotch tape pull up on the plastic connector that holds it in and pull the ribbon out then get a clean pencil eraser and gently clean the ribbon and put it back in dont forget to push the locking tab back down then try it again and let me know

SOURCE: cancel light and rinse only light keep blinking and wont start

Hello,

Hopefully you have resolved your issue. I have not heard of the cancel light flashing issue. I have had problems with the clean light flashing seven times over and over and the control panel will not operate. Here is the solution to that. Maybe it will work for your issue as well.

Open dishwasher door,
Push Hi Temp Scrub button,
Push Saver Dry button,
Push Hi Temp Scrub button again,
Push Saver Dry button again,
All lights on control panel will come on.
Close dishwasher door,
Push Baked on Cookware or Normal Button.
Dishwasher should start and complete cycle.

It is good if you have kids that play video games. Their fingers are used to pushing buttons quickly. I guess this resets the control board. The service guy let me have this info as I used to deliver appliances and work on them somewhat.Hope this helps.

Good Luck,
Tom

SOURCE: My normal cycle and cancel button lights are

Probably a keypad gone bad. Try replacing the keypad.

There is a troubleshooting guide behind the foot kick panel. It gives a sequence to test for a bad keypad. You can try that sequence to be sure.