An increased flap angle will allow a reduced rotate speed which will, despite the greater drag due to the flaps and thus reduced acceleration, result in a reduced take-off ground roll (take-off run). However, the climb gradient after take-off will be reduced by an increase in flap angle, both maximum gradient and all engines operating gradient at scheduled climb speed, typically V2 + 10 kts. (Note that V2 will often be lower with an increased flap angle).
I suspect that the "take-off distance" referred to in this question refers to the distance from brake release to an (unspecified) height. If this height relates to setting climb power or beginning the acceleration for flap retraction, the take-off distance may well be increased due to the reduced climb gradient.