Just something I thought of - have the LFM panel provide some sort of warning that a character is not flagged for a quest in the same manner it does that they do not own the content. This would only work, of course, if the leader selected the quest from the list before putting up the LFM. This would prevent newer players from purchasing the content then attempting to join a raid they are not flagged for. Just as it is irritating to fill a party full of people only to find out upon zoning into the quest or running to the quest that some members do not own the content, the same is true for quests which require flagging, usually amplified since you are often dealing with a raid party. I have been in many raids where we fill, step in, and then find out someone just purchased the pack to run this quest or recently purchased it and has not really done much with it and is not flagged.
The manner in which the warning could be displayed could be as simple as a flag icon next to the quest that is either green for flagged or red with a circle around it and a line through it to a pop up box when the player attempts to click on the LFM (similar to the "bind" warning) warning the character they are not flagged, giving them the information that they need to flag, and then asking them if they are sure they want to click the LFM. Granted, they could always still click "yes" and be put into the queue but no one could say they were not informed. I am in favor of the latter pop-up box because it not only requires an affirmative click (as opposed to just ignoring the icon) but also informs the player of what they need to do to flag so there is no confusion.
Just a thought