I define "fuck you money" as having sufficient income that you don't need to work any particular job to pay all your expenses, or even be careful about not burning bridges. If you have "fuck you money", when you get the memo about the new TPS report cover sheets for the 5th time, you can literally say, "Fuck you: I quit," and walk away.
The exact amount required depends largely upon your expenses and lifestyle. If you are fine with living in a van down by the river, it might be only $100k. If you like things like showers and flush toilets, you may need $1M. Think of it like a suspended early retirement. If you are working, it is because you want to, not because you need to.