In addition to double-button (or center button) clicking to rapidly clear fully flagged numbers, there are other clicking techniques that may be used in Minesweeper. With practice, these techniques can help improve your times.
A popular technique in Minesweeper is known as "chording". Some of the fastest times ever accomplished in Expert level have been said to be achieved with this technique. A strafe is performed by using the following steps: 1) Flag a cell by pressing, but not releasing, the right mouse button, 2) drag the mouse, with the right mouse button still pressed, to a number that is fully flagged, 3) with the right mouse button still pressed, press and release the left mouse button to clear the fully flagged number.
Chording promotes an alternating right-left mouse button style of play. For instance, you might flag 8 or 10 cells with the right mouse button, and then keep the right mouse button pressed on the last flag. Then you may use the left mouse button to clear several fully flagged numbers, as you drag the mouse around with the right mouse button still pressed.
The animation below illustrates the chording technique.
Playing Without Flags
While playing without flags may seem bizarre at first, there are some advantages to be considered. First, clicking to mark a cell with a flag costs a click. There are situations where the flag/double-button click technique does not save clicks over manually clearing each safe cell with a left click (and not flagging the cell with the mine).
Second, when using flags, you have to think about which cells are mines (so you can flag them), and which cells aren't mines. When playing without flags, your focus is only on cells that do not contain mines. After all, the object of the game is to clear all the cells that do not contain mines.
This technique is difficult because it removes the visual cues about where mines are located. However, it does exercise your brain and with practice could potentially be very fast.