A group of employees who should be working, but instead are either:
1. Standing around doing absolutely nothing
2. Doing something very obviously NOT work
...on company time.
1. 'Water cooler' conversations with more than 2 people for more than 3 minutes are considered a dog fuck party.
2. Pigs at the donut shop, pigs in the parking lot sitting in their cruisers, pigs doing pretty much anything is considered a dog fuck party.
It is to emphasize the word "fuck." It comes from the shorter version of "give a fuck" and then "give a flying fuck." It means "I don't care" but with emphasis. So it is an emphatic "I don't care!" Or also, emphatic "I could care less."
"I don't give a flying dog fuck if you want to go to the beach, we are NOT going!"
"I don't give a flying dog fuck if you like driving, I am doing the driving!"