Occasionally when turning the ignition on I get about 10 quick chirps of the warning beeper and the red park brake light flashes quickly. There were no unusual messages when the park brake was applied the night before. The light continues flashing if the engine is started, turning off and on results in the same pattern. Putting the park brake off extinguishes the light, putting it back on results in a solid park brake light, no flashing.

There aren’t any messages displayed in the message console, is it trying to tell me something?
Doesn't seem to be a problem that I can detect, maybe the EPB just isn't on firmly after the components have cooled down?
(57 Vogue SE TDV8)

Mine did the same - been back to the dealer a few times - been adjusted but didn't fix it at the moment it is with them and they have diagnosed (and are replacing) the actuator. Will see.

Mine did this once when I adjusted the suspension height with the parking brake on. I'm sure the user handbook suggests not to do this: ie disengage parking brake before adjusting suspension height.
Do you park your car in 'access mode' or did you on that occasion? 
Had it, loved it!
2007 Vogue SE TDV8
Stornoway Grey / Ivory
Climatic Seats, RSE, AFS, Deployable steps, iPod kit.

I don't remember seeing the light flash any time I have used access mode, but I very rarely use that.

Good thought tho, if the suspension does adjust itself over night then it could change the tension on a cable as I think the park brake works on the rear wheels. Classic and P38 RRs had a park brake drum on the back of the transfer box, so that wouldn't be effected.