Yellow Flame vs Deep Yellow

How close are they?

ΔE 23.3, loose: different enough that you should pick on purpose. Deep Yellow is more saturated, cooler than Yellow Flame.

Can I use Deep Yellow instead of Yellow Flame?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Deep Yellow is more saturated, cooler than Yellow Flame.

Can I use Yellow Flame instead of Deep Yellow?

The same difference applies the other way round: Yellow Flame is more muted, 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.