ΔE 15.9, loose: different enough that you should pick on purpose. Mars Orange is noticeably darker, cooler than Flickering Flame.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Mars Orange is noticeably darker, cooler than Flickering Flame.
The same difference applies the other way round: Flickering Flame is noticeably lighter, 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 Mars Orange on the colour wheel
All matches: Flickering Flame equivalents · Mars Orange equivalents