What size fuse if any is backing up the MCB ? The short answer is it will most likely be fine in practice, but I point out that if  5,99kA is a spot reading on one day, it will be higher or lower on another day or even on another reading the same day - that level of precision is simply not reliable. A 6KA breaker is only guaranteed to survive breaking  a vey few dead shorts on such a supply - but how credible is the dead short fault ?

And if there is for example a 400A fuse behind it, then that will probably cut off as well, so limiting the damage to the breaker.

Mike.

There is a MCCB NSX 160N. 

My main concern is the highest value when I tested this DB the PEFC was 5.99 kA  and this installation is 3 phase this value need to be multiple by 2 and the Ipf for this is 12 kA  and the designer and electrical contractor for this installation told me that it is just a isolator switch and the breaking capacity is not important as the circuit breakers have a breaking capacity 10KA and these should be protected the installation.

OK, so you made a single phase L-E  or L-N test, and got 5.99kA.  That is too close to the knuckle to be sure which side of 6kA it is really,  (as tomorrow  it could just as easily be 5kA or 7kA...) 
And using the 'double it' rule of thumb,  if there was ever a "silver nail"  low resistance phase to phase fault in the wiring close to that breaker,  and no other fuse or breaker opens first, it looks like the breaker will not survive more than the one event, and will need replacement.

Usually, however, there is nearly always  something else that operates as well -  a fuse where the incomer comes into the building,   or even just the fuse back at the substation, that will operate if the breaker welds closed or is not fast enough for some reason. 

Of course if that goes, and cannot be reset until the charred remains of the breaker are swept up and replaced, that is a serious disruption to supply, though perhaps a very unlikely one. Hence my question about what supplies it and what else is affected.

That may be an acceptable approach, sometimes, but the person who took that design decision needs to understand the implications.

(For example  a 6kA breaking MCB  behind a 100A house service fuse on a supply with a 19kA PSSC is  usually  considered OK - in the worst case, the house service fuse operates, and limits the damage to the MCB....)

Mike.

OK, so you made a single phase L-E  or L-N test, and got 5.99kA.  That is too close to the knuckle to be sure which side of 6kA it is really,  (as tomorrow  it could just as easily be 5kA or 7kA...) 
And using the 'double it' rule of thumb,  if there was ever a "silver nail"  low resistance phase to phase fault in the wiring close to that breaker,  and no other fuse or breaker opens first, it looks like the breaker will not survive more than the one event, and will need replacement.

Usually, however, there is nearly always  something else that operates as well -  a fuse where the incomer comes into the building,   or even just the fuse back at the substation, that will operate if the breaker welds closed or is not fast enough for some reason. 

Of course if that goes, and cannot be reset until the charred remains of the breaker are swept up and replaced, that is a serious disruption to supply, though perhaps a very unlikely one. Hence my question about what supplies it and what else is affected.

That may be an acceptable approach, sometimes, but the person who took that design decision needs to understand the implications.

(For example  a 6kA breaking MCB  behind a 100A house service fuse on a supply with a 19kA PSSC is  usually  considered OK - in the worst case, the house service fuse operates, and limits the damage to the MCB....)

Mike.