Where did you read that about flash games? If it's of acceptable quality as stated per the game request rules and moderator discretion, it'll be on the site.

Taken from the "request game" page:

[quote]At this time, we are not adding the following: Short/Trivial Games, Generic Puzzle games, Visual Novels, PvP-related activities, High-Score based submissions, and Non video-game activities. We also are not adding generic typing games, vocabulary games, math games, geography games, basic quizzes, generic sudoku solvers, generic Minesweeper remakes, generic Rubik's cube solvers, and similar content. If there are 100 flash games with similar content, we're probably not looking to track them. If there is a notable commercial release of a game like this, we may track it.[/quote]

You can request web games, with flash or not. But those kind of games are looked at with more scrutiny, and generally many of them will not be accepted because they are too short or trivial.

You can search "the site" forum about it, there are many threads about this subject.