Does the initiative from flux missiles apply to just the missiles or the whole ship?
I believe that they are intended to apply to the entire ship. I've come to this conclusion for two reasons:

First, the text of the ROTA rulebook reads:


  Two modified Ion Missiles capable  of warping the flux grid, giving two Initiative.


If they were intended to apply only to the missiles, it seems likely that it would be indicated in this text.

Second, the energy cost is only one of two costs related to a technology: you should also consider the research cost. The research cost of a Plasma Missile is 14/7, whereas the Flux Missile is 11/8. Comparing this to the Ion Cannon (no research cost) and the Plasma Cannon (6/4) shows us that the price difference on the missiles is half that of the cannons. That, it seems, is where you're paying for the increased initiative.