The request of the captain is for Jim to bring him rum. Jim does not want to do so because it is strictly against the doctor's orders for the captain to drink. Here is an excerpt from that exchange:

Jim, you'll bring me one noggin of rum, now, won't you, matey?"

"The doctor—" I began.

But he broke in cursing the doctor, in a feeble voice but heartily. "Doctors is all swabs," he said; "and that doctor there, why, what do he know about seafaring men? I been in places hot as pitch, and mates dropping round with Yellow Jack, and the blessed land a-heaving like the sea with earthquakes—what to the doctor know of lands like that?—and I lived on rum, I tell you. It's been meat and drink, and man and wife, to me; and if I'm not to have my rum now I'm a poor old hulk on a lee shore, my blood'll be on you, Jim,