Throughout this thread, you'll find a lot of denial, sometimes based on different playing experience, but sometimes also on rules misperceptions. This lists tries to clarify the latter. I already once did a
summary after 32 pages.
Basically, many posters started their criticism based on assumptions that by now I proved to be false. And still they never change their views, which is in part responsible for the length of this thread.
NOTE: For general monk and core game misperceptions and fallacies (imo) check below the chapter II.2. "Monk Myths"
1. Can the monk flurry his grappling checks?
Yes. More grappling attempts are based on base attack bonus, and the monk's flurry results in a modified base attack bonus (see the monk class description). Check also the 3.5 FAQ p. 20 which clearly outlines grappling as a possibility in a flurry to do in place of an attack.
And for those remaining doubters,
Lord Silvanos is quoting the Rules Compendium to support the notion that you can flurry in a grapple.