How does a flex takeoff increase fuel consumption compared to a TOGA takeoff?
Fuel consumption for the flight will be slightly higher when carrying out a reduced thrust takeoff.

Simply put, the flight is operated at lower, less efficient altitudes for a tiny fraction longer, so less time is spent at more efficient altitudes. It’s a rather small amount, but nonetheless measurable.

From Airbus‘ Getting to Grips with Fuel Economy:


  Compared to a full thrust take-off, flex thrust will generally increase fuel burn. The increased time at low level offsets the slight reduction in fuel flow induced by the lower thrust.


The source goes on to list typical fuel burn increases, e.g. for an A320 it’s 1kg (!) when taking off in CONF 1+F and 5kg in CONF 2.