I'm guessing the downwind checks are something like BUMPFICH? Flaps shouldn't really be a downwind check in light aircraft, they are something to deploy as and when needed (hence 'as required' - read 'who cares'). Others will no doubt have different opinions but F to me means Fuel - quantity, balance, pump etc.
An exception however will be if your FTO is geared towards commercial training, then they will want to get you accustomed to deploying flaps at a particular stage in the approach, as happens with airliners etc.