I am not claiming to speak for the community as a whole, so this is more or less just my personal opinion. However, I would like to think I share these onions with most of my fellow players.
So, with that in mind, here is my crack at general rules that should always be followed in group content. I try to follow this model when I play, and I enjoy it when everyone else does as well. (It's a bit long, but consider the highlighted heading to be the tl;dr; as the subsequent paragraph is simply me reiterating/expanding on the rule.)
1) Thou shalt have fun.
This is a game we play for fun people, and you should always keep that in mind. These commandments all center around this one concept. Let's make the game as fun as possible for as many people as possible. Without that, nothing else matters.
2) Thou shalt stay respectful and civil at all times.
My father-in-law likes to say "Don't argue with a pig. The pig will enjoy it, and you'll get dirty." No matter how much the person you are talking to may deserve a good tongue lashing, it's not worth it. If you can't resolve a problem in a civil manner, Report, Ignore and Kick are your friend. Select the appropriate one, and move on to enjoying the rest of the game. (See #1 above.)
3) Thou shalt help thine fellow player learn the flash point.
Always keeping #1 and #2 in mind, you should try to help out new and inexperienced players learn rather than complain (or just quietly stew) over the fact that they are not running as efficiently as they could. This is how new and inexperienced plays become experienced veterans and help others, and it's a cycle worth preserving and building.
4) Thou shalt alert thine group if thou hast not done the flash point before.
Similar to #3, if you are new to a flash point, make sure your group knows. No need to go on about it, as it's usually sufficient to just say something like this when you enter the instance: "Hey guys, just so you know, I've never done this one before, so if there's anything I need to know, feel free to point it out." You will usually find people happy to help out where needed, and more forgiving if they know you are learning and trying.
5) Thou shalt not roll Need unless Needed.
If the drop is equipable for your current character, and better than what you have, "Need" is appropriate option. In any other case, "Greed" should suffice. Even if your companion needs it, or an alt needs it, or you just want to sell it because you think you are getting shafted on drops. Need should be the exception, not the rule.
I know a lot of people argue about this, but to me it seems pretty straight forward. If you are in a group or see a player operating differently, reference rules #2 for how to deal, and always keep #1 in mind.
6) Thou shalt let people watch the cut scenes in story mode.
When doing level appropriate story mode flash points, the default response should be to watch all cut scenes unless the entire group agrees to skip before beginning. In story mode, odds are good someone has not seen the content or would like to watch it again, and they should be given the right to do so if they want, even if three others would prefer to skip.
7) Thou shalt skip the cut scenes in hard mode.
Similar to #6, skipping the cut scenes should be the default for hard mode flash points unless the entire group agrees to watch them before starting. If you have not seen the content, go watch in story mode even if you are over leveled. Most flash points can be soloed at level 50 if there is no other option. I sympathize with people who want to watch it every time, as I am one of them, but hard mode flash points are primarily for people trying to gear up, and that should be respected.
8) Thou shalt not rush ahead unless thine group has agreed to a speed run.
Leave Leroy in the other game, and wait for your group to assemble before rushing into the next fight. If you want a speed run (where the default is to rush as fast as possible all the way through) make sure your group agrees in advance.
9) Thou shalt assist thine group in any way possible, not just by sticking to your assigned role.
Obviously make sure you are fulfilling your main role first. That said, just because you are a healer or tank doesn't mean you can't throw out the occasional interrupt/DPS burst. Just because you are DPS doesn't mean you can't pull agro off the healer or toss a heal yourself if they are having trouble keeping up. Fundamentally, flash points are about team work.
10) Thou shalt remember to thank your group when exiting.
This should be a no-brainer, but a lot of people seem to forget it, especially if the group has not been the best they've had. Always remember #1 and #2.
Well that's my take on it anyway. Feel free to update, append, or add your own.