ΔE 22.1, loose: different enough that you should pick on purpose. Flaming Forge Orange is noticeably lighter, much more saturated, warmer than Barren Yellow.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Flaming Forge Orange is noticeably lighter, much more saturated, warmer than Barren Yellow.
The same difference applies the other way round: Barren Yellow is noticeably darker, much more muted, cooler.
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 Barren Yellow on the colour wheel See Flaming Forge Orange on the colour wheel
All matches: Barren Yellow equivalents · Flaming Forge Orange equivalents