Considering that BP doesn't even bother measuring how much oil is spilling
Well, I'm pretty sure that they have a rough idea, and it's way more than what they're saying in public. They just don't want to formalize their estimates, because then they'll have to report the numbers. I did some napkin (units(1)) calculations based on the volume of dispersant that they say they've been using and, if they're using at the suggested dilution, then at a minimum they're dealing with 60K~500K barrels per day.
((don't have the actual calculations on hand, right now, and I'm on a different computer, so I can't even just look at my command line history))
And that's a minimum.... the volume that they're using may be limited by the supply chain.
I'm guessing that, in internal conversations, they're duck-speaking their way around solid numbers... For example, they can talk about how much dispersant they'll need ( a number based on oil flow), but there's probably an unwritten rule about never mentioning the oil flow estimate that underlies that calculation, because it'll be seekable in disclosure requests, and they'll still be able to 'truthfully' claim that they've never talked about the actual oil flow.