Your objective, in the end, is to touch down at the correct speed at +/- the correct point on the runway. This is valid for all aeroplanes: the C172 as much as any.
To achieve this, the power reduction becomes a factor of how close you are to your optimum path and speed, and what the trend of those two parameters are. It may sound obvious, but if you're slow and steep, you don't want to pull the power early, as you'll need the energy in the flare to arrest the descent before stalling. If you're fast and shallow, you need to bleed energy off, as you have plenty and little is required for the flare.
So it's all about judging how well your approach went by the time you approach/pass the threshold. A few extra knots? Pull the power early, anticipate the pitch down, and be prepared for a correction to this and then a flare on top of that.
Lagging behind the power curve a bit? Keep the power in in longer.
Anticipate the lessened need for pitch changes and don't over-flare as it could easily result in ballooning.
Steeper approaches are more difficult, and will bite you to a greater extent than a shallow approach, so be mindful of the PAPI or GS angle when going to different fields.
Being high or low to start with should really have been corrected earlier, although when you gain more practice, you can do "last-second" corrections to this too.
This judgment will take a while to develop, and mature with experience. However, it seems like most students and instructors like to fly the C172 on the conservative side of the book - ie with higher approach speeds than what the book says, and using these speeds there is normally sufficient energy to pull the power early (say, when the threshold disappears below the cowling).
So to sum up: be mindful of your planned approach speed and watch it as you get close to touchdown. Then decide on when and how fast to pull the power, and that in turn will dictate your flare technique. Nail it every time - and remember that a good landing is at the correct speed and at the correct position - sometimes it will be a greaser and sometimes... well, sometimes it's just another safe landing!