We have to consider the elements of the lift formula.
L= CL1/2 rho v2 S
When we increase flap, S gets bigger in our formula. We generate more lift so
we can get airborne earlier and increase the FLLTOM.
Getting airborne earlier will increase the stop distance available, in other
words V1 will be a slower speed at take-off flap compared to zero flap.
Look at the difference (CAP698 pg 64/65) in the V1 speeds for
40 tonnes Flap 5 which is 113kts and 40 tonnes flap 15 which is 104kts.
Similarly check out the Vr speeds at flap 5 it’s 114 kts and flap 15 107kts.
What we can do with this on a limiting runway is to increase
the mass until we are again on the limits for TORA, TODA and ASDA.
Increased flap increases profile drag and reduces the climb gradient so we
would have to check out the effect of the increased flap on the climb limited
take-off mass.