I don't claim to be an expert in all this, but over several years of securing M+M, Upgrade, Companion and Reward flights, I've built up an idea in my mind of how it all works.
I believe that Flying Club is a loyalty programme which offers genuine benefits. We have been successful in securing either M+M, Upgrade, Companion or Reward flights for all our trips for a good few years now. However, that's largely due the fact that we've been willing (and able) to be flexible. For example, we extended our upcoming trip by two days either side of that originally planned to secure PE Companion flights.
What you need to understand is that there are many classes of ticket sold for any given flight. Each class is assigned a code (these codes apply industry-wide, but their use can differ from airline to airline). There will only ever be certain numbers of seats, per flight, available in each class. For the M+M, Upgrade, Companion and Reward flights there are very few (although ordinarily it appears there is more M+M availability than the other categories). Class G, for example, is used for Reward or Upgrade flights in the Upper Class Cabin. Class T is used for Reward or Companion flights in the PE Cabin. The numbers of seats in these classes will be decided on a flight-by-flight basis. That is why you will often be unable to secure such seats even though the flight is far from full.
One time (before I understood any of this) we phoned to enquire about both Companion and Reward flights in PE. We were given prices for both options and, based on the miles we each had available, decided that our friends would book Companion and we would book Reward. They phoned and booked theirs and then handed the phone to us to book ours. It transpired that there were only 2 seats available in that class on that particular flight. They, of course, had already taken one of those seats, so there was only one left for us to book.
We phoned last week to enquire about Companion and Upgrade (UC) flights for next August. We wanted to fly into Boston and out of Orlando. We could secure either option with no problem for the LHR-BOS leg, but not the MCO-LGW one. We started by trying to move the dates to see if that would make a difference, but (the very knowledgable and helpful) Lee in the Premier Team explained that they don't normally allocate any seats in those codes on any route out of Gatwick - there are only 14 UC seats on those aircraft, so they tend to sell them easily. If there are any unsold seats 7 days before the flight, there's a chance they will release some.
I hope that helps a bit. In summary, for the best chance of securing one of these fare codes, try to be as flexible as possible and to book as early as possible.