The flap load relief function is controlled by the FSEU. This receives airspeed information from the left ADIRU. This gets static & pitot pressure inputs from the left air data modules (ADM).
So, if the Capts pitot probe and/or static port are u/s, the flap load relief function will not be available. This does not prevent you from using flaps but you will have to monitor airspeed from the F/O’s instruments.
Your scenario of extending the flaps “far into the red” is, I would hope, unlikely as you will have noticed the high speed from other clues - F/O’s insts, airflow noise, control feel etc. If you were to extend flap at high speed you would run the risk of damage or detachment which, if asymmetric, would cause large amounts of roll.
I have not got the link to hand as I post this, but search the internet for “N520UP AAIU Report No: 2004-004” which describes a 747 with static port problems on a post maint airtest.
S&L