A320 Engine Failure After V1
 

The FCTM states that the flight crew must delay the acceleration for securing the engine. What exactly is the reason for it? Is it just to manage the tasks on priority?

Securing Failed/Damaged engine is first priority to prevent further complications from it. Acceleration to clean up and resuming climb is to maintain certain gradient profile for terrain clearance. There are two limiting altitudes for acceleration, the minimum and maximum. By exceeding the minimum acceleration altitude the gradient of climb profile is not affected. But the maximum should not be exceeded as it will cause 10mts limit on takeoff thrust to be exceeded.

Does the 10 min limit apply to a flex take off? Or is it only TOGA?

Unlikely it would ever really be noticed in reality. More important priorities to deal with. I remember on my previous type (setting MCT manually) would often be an increase in thrust after a high assumed temp take off. Hence my question. Is there any way of knowing when the take off flex is equal to or exceeds MCT?

It applies to both.
You have only one procedure common to every take off you do - flex or TOGA and everything in between.
KISS.

Procedurely the limit is on takeoff thrust whatever was used.

Airbus put a lot of thought into the recommended procedures and they work. Why try to reinvent the wheel?

Yep. This procedure was only introduced about 8-10 years ago.