I did this once, but didn’t literally give the finger, I put a 5 page essay describing everyone’s dirty laundry in the mailboxes of the company owners managers, I bet that they had some fun conversations. The place was an OSHA nightmare, and I concluded my essay on that point, hopefully it saved someone from getting hurt/killed…
But that was at a non-career related job out of college and I never would have used them as a reference.
In your case, if it were me, I would give them a month and prepare for their response. I would also consider providing a list of people you could refer to take your place if you know any, and offer to assist them in training folks there or in the recruitment of your replacement.