ΔE 24.7, loose: different enough that you should pick on purpose. Burnt Orange is a little darker, much more muted than Flickering Flame.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 25). Burnt Orange is a little darker, much more muted than Flickering Flame.
The same difference applies the other way round: Flickering Flame is a little lighter, much more saturated.
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 Burnt Orange on the colour wheel
All matches: Flickering Flame equivalents · Burnt Orange equivalents