No reason why the _ctrl is not const. I just copied it wrong.
I think that the _centroidExtractor and the _flagHandler should be on the CircularApertureFluxAlgorithm, since to me it goes logically with the SimpleAlgorithm. And ApertureFluxAlgorithm is not a SimpleAlgorithm. But if you are confident that all ApertureFluxes are going to follow this pattern I can move it.
I put the SincCoeff initialization in CircularApertureFlux because that is where you had it. I think it belongs in ApertureFlux.
The initialization of FlagKeys does not belong in CircularApertureFlux. My mistake. The code is a duplication. I put it there by accident when I was removing the FlagHandler array I had put in to CircularApertureFlux. (your recommendation that we not try to do this now).