ΔE 17.8, loose: different enough that you should pick on purpose. Fire Orange is a little darker, more muted, cooler than Flickering Flame.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Fire Orange is a little darker, more muted, cooler than Flickering Flame.
The same difference applies the other way round: Flickering Flame is a little lighter, more saturated, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Flickering Flame on the colour wheel See Fire Orange on the colour wheel
All matches: Flickering Flame equivalents · Fire Orange equivalents