There are two crew oxygen bottles in the forward cargo compartment, situated in the cargo compartment sidewall just behind the forward cargo door. A pressure reducer reduces the bottles high pressure of up to 1850 psi to a medium pressure. A single medium pressure line goes forward and upward through the sidewall of the maindeck to the cockpit, where another pressure regulator is situated behind the coat rack. After the pressure is further reduced to ± 100psi, the system splits up in 4 lines to the respective crew oxygen masks.
So as it appears that the captains oxygen supply was compromised (ie. burned through) with the First Officer apparently still having oxygen, the fire must have progressed
inside the cockpit area, as that is where the system splits up.
This story just goes from bad to worse...
As far as keeping smoke out of the cockpit:
From the B777 FCOM:
777F
The flight deck and supernumerary cabin receive 100% fresh conditioned air from the left pack. To prevent smoke and objectionable odors from entering the occupied compartments, the flight deck and supernumerary cabin are maintained at a slightly higher pressure than the main deck cargo and lower cargo compartments.
Unfortunately, the worlds most popular widebody freighter doesn't have it set up like that.