ΔE 15.6, loose: different enough that you should pick on purpose. Transparent Brown Iron Oxide is noticeably darker than Demigod Flames.
Can I use Transparent Brown Iron Oxide instead of Demigod Flames?
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Transparent Brown Iron Oxide is noticeably darker than Demigod Flames.
Can I use Demigod Flames instead of Transparent Brown Iron Oxide?
The same difference applies the other way round: Demigod Flames is noticeably lighter.
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.