Have you marked your kitchen as Staff Only or have Staff Doors the only way in? Your prisoners need a route to the kitchen that isn't blocked by one of those things. Switch the kitchen to general (or whatever the white space is called) and install regular doors, and you should be fine.

How er, are you supposed to view time lapse videos?

The problem I have with my entry into the prison has to do with my cooks. I don't like making my cooks wait for guards to open jail doors for them when they leave the kitchen to pick up supplies from the Deliveries area. So to stop that, I usually put in a staff-only door and staff-only corridor lea...

I have the exact same problem.