ΔE 25.5, loose: different enough that you should pick on purpose. Old Rose is a little darker, much more saturated, cooler than Dead Flush.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 26). Old Rose is a little darker, much more saturated, cooler than Dead Flush.
The same difference applies the other way round: Dead Flush is a little lighter, much 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.
See Dead Flush on the colour wheel See Old Rose on the colour wheel
All matches: Dead Flush equivalents · Old Rose equivalents