I agree with Tony as you are separating the two leaves which improves impact noise reduction. If you can afford it, also use acoustic wall ties between the leaves as this can be a major area of sound transference through this construction. Particular attention also needed where your new wall meets existing construction to avoid 'flanking' sound transfer.

Hi Daniel,
I am not an acoustician so cannot give specifics for your situation, but as a rule of thumb, adding mineral wool insulation within the cavity will definitely increase thermal/fire performance whilst possibly not adding anything further to the acoustic properties of the wall. Rockwool batts are unlikely to make it worse however so the acoustic engineer you spoke to may have been approaching the issue purely from sound transfer relative to wall build up.
I wouldnt bother too much with the Rockwool Flexi in a standard masonary cavity though, your paying extra for it to be able to squeeze into framed construction which you won't need sandwiched between two leaves of blockwork, standard batts will do. As mentioned before, make sure there is a tight joint at the abutment with existing or all the hard work could be undone.