I have Eight current carry conductors in a raceway flexible metal conduit. 4 # 8 THHN 4# 10 THHNth 1 # 12 grnd. I am derating at 70% based on 310.15 (b) (3) (a) using table 4 and table 5 in chapter 9 what is the minimum size flex i can use. My over current protection in the panel is 20 amp. The wire size has been increased due to voltage drop.
Assuming that CCC's is your only adjustment.
So you are telling us you have 8 CCC's (limited additional information)...
8 AWG THHN is 0.0366 x 4 = 0.1464 in2
10 AWG THHN is 0.0211 x 4 = 0.0844 in2
12 AWG THHN is 0.0133 X 1 = 0.0133 in2
Total is shown = 0.2441 in2
Total size of the FMC should be no less than Trade Size 1
Now....did you need to increase the EGC...and would it make a difference in the sizing........?.....That I have not considered as it was not asked.
If an 8 AWG EGC is considered it would change the in2 totals to 0.2674 in2 resulting in a Trade Size 1 - No Change.