Litebulbs - Yes I'd expect the process to flow back through the flight deck. Examples of feedback that could go up the chain of command could be "Was information related to delays conveyed in a timely manner", "Did you feel supported in your work", "Do you feel the Captain led by example" "Did you feel any concerns you raised were treated seriously" and so on. It doesn't take much to structure some questions which cut to the nub of what makes effective teamwork on board and the non-tech skills which BA Flight Ops training department have been pushing for years provide a ready framework for such a structure.
Ottergirl - I don't doubt you are used to receiving feedback. However some of your colleagues display a distinctly less mature response to negative feedback and instead sulk for the remainder of the trip and spread dissent amongst the crew. I've seen it.