ΔE 9.1, close: similar, with a visible difference side by side. Blazing Ink is a little lighter, cooler than Flickering Flame. They are different kinds of paint: Army Painter Flickering Flame is an opaque base/layer paint and Formula P3 Blazing Ink is an ink, glaze or transparent paint, so they won’t behave the same on the model even where the colour is close.
Usually, if you are not matching paint already on the model. Close match (ΔE 9). Blazing Ink is a little lighter, cooler than Flickering Flame. They are different kinds of paint.
The same difference applies the other way round: Flickering Flame is a little darker, 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 Blazing Ink on the colour wheel
All matches: Flickering Flame equivalents · Blazing Ink equivalents