Go to Settings/Display/Screen Timeout, and click "Never Timeout".
Then, open the kickstand, and adjust the night brightness high(er), via the Menu/Settings. You have to do it as soon as you open the kickstand, before it disappears.
After that, you should be able to have the clock on display the whole time you have it set in kickstand mode.
Also, if you have it on the charger, it won't time out on you, and you can see your clock. I have my display set to go off after 1 minute in normal mode, but when plugged in and kickstand out, it functions as my bedside alarm clock (with the night brightness setting set low, of course).