ΔE 40.4, loose: different enough that you should pick on purpose. Red Cloak is noticeably darker, much more muted, warmer than Doomfire Magenta.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 40). Red Cloak is noticeably darker, much more muted, warmer than Doomfire Magenta.
The same difference applies the other way round: Doomfire Magenta is noticeably lighter, much more saturated, 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 Doomfire Magenta on the colour wheel See Red Cloak on the colour wheel
All matches: Doomfire Magenta equivalents · Red Cloak equivalents