My bet would be the coil, the PCM, and the interconnectig harness in that order.
Coil # 3 fires cylinders # 2 & 6, all of which have codes. Sounds like a dead coil section.
The P0171 & P0174 may or may not be related to the greater current failure. Fix the big one first, get it going, then see if these codes come back, addressing them if required.
The flashing CEL indicates a major misfire, one that is capable of damaging the engine. Don't run it.
Clear the system of fuel as described and see what happens.
Steve
