Many Ways to Kick a Drum
Forget the 'flat foot vs. toe' argument. When it comes to working the bass drum foot pedal, pretty much anything goes. All of the pedal techniques listed below have advantages and limitations. My advice is to try them all, as each one can bring something worthwhile to your bass drum execution. Note that some pedals may not be suitable for certain techniques.
The most basic of techniques, the foot remains flat on the foot plate at all times. This is a good choice for slow and low volume playing, although it can deliver respectable volume and speed. It also provides excellent control over rebound and some players prefer having a bit of contact with the floor.
The simplest approach to toe technique is to keep the ankle relatively fixed and use your leg muscles to do the work ... i.e. a stomp. This delivers lots of volume and can be less fatiguing but is limited in terms of speed and articulation..
This technique uses mostly the ankle with the upper leg joining in with a bounce. With the heel about 1 inch from the heel plate, tap with the toe. Some practitioners like to swing the heel from side to side between strokes.
Moeller ... sort of
While Mr. Moeller never wrote about working with pedals, his basic principle can still be applied. The next two styles use a Moeller-like double kick that can propel you to fabulous speeds once mastered.
1. Steve Gadd Kick
This technique begins with the toe near the middle of the foot board with the heel slightly raised. Tap the pedal with the toe and immediately shift the foot forward, catching and kicking the pedal during the rebound. Great for doubles, shuffles and sambas.
2. Heel-toe/Two Step
This one is a bit like the old 'heel-toe' hi-hat technique. The first note is played on the back half of the pedal with the heel. The second note is played by catching the footboard on the rebound by dropping the toe. The resulting rocking motion is great for doubles, triples, and raw speed. Almost required for some metal music. (May not be possible on certain pedals.)