I believe you submitted the wrong model number. The Kenmore dishwashers that start with the prefix 587 does not blink the Clean led. Some of the Kenmore dishwasher models that start with the prefix of 665 do.
The blinking "Clean" led indicates that the dishwasher did not detect a water temperature rise while the dishwasher was supposed to be heating up the water or it could mean some other failure depending on the exact model.
On most models of Kenmore dishwashers, the clean light flashing indicates a problem with the heater circuit. If this is the first time that this fault has occurred, you may be able to reset it and continue to use the dishwasher. If the heating element is working properly and you have no component failures in the dishwasher, then the control will resume normal operations after the reset procedure. If you have a problem, then the fault will resume and you will need service from a technician.
To reset this fault code, press the following buttons within 5 seconds in this order: HEATED DRY, NORMAL WASH, HEATED DRY, NORMAL WASH. The dishwasher must be in standby with the door closed when these buttons are pushed. All of the console light will turn on and then the dishwasher will begin a quick diagnostic cycle. You can cancel this cycle by pressing the CANCEL/DRAIN button. The dishwasher may begin a 2 minute drain cycle. After this process, the control will be reset. You should be able to program a new wash cycle. Check your heater element for proper operation and monitor the dishwasher to make sure it is operating correctly. If the fault returns or you detect problems, call a service technician to diagnose and repair the dishwasher.
If this information does not help, resubmit your question with the full model number of your dishwasher and additional details.