The context flags depend on which context you are using, but you can get the ones for the current context by using
warn join('<BR>',lex_sort(Context()->flags->names));
in your problem file after you select the context. There are also some tools in pg/macros/PGinfo.pl for listing the flags and their values, or the entire Context() structure.
As for the cmp() flags, that is harder, since each MathObject class has its own set, and there is no one place where they are all listed, even in the code itself. Many of the most common ones are in the documentation at
http://devel.webwork.rochester.edu/doc/cvs/pg_HEAD/doc/MathObjects/MathObjectsAnswerCheckers.html
so that is the first place to start. As you have found out, the documentation on MathObjects is something that needs improvement.
Davide