I think that the confusion may be arising from a definition of TO "distance".
Is Take-Off Distance Take-Off Roll? Or is it the distance required to acheive a certain height to clear an obstacle and/or achieve a height of 400ft AGL?
In the book "Aircraft Performance Theory for Pilots", (P.J. Swatton), they define take-off distance as:
"The distance from brake release point to the point at which screen height is attained."
Does this change our answer? Is the question -in- question, refering to a different definition?
I tend to think that anywhere a climb of any amount is required the ground distance to a particular height will increase with flaps. But then again, does the decrease in ground roll compensate for the slower rate of climb to the defined screen height and therefore produce the same net climb ratio from point of brake release?
VRT