I must admit your post does echo some of my feelings and experiences with flashpoints, to the point I almost gave up on them. Even story Heroric 4 or 2+ missions, my heart sometimes sinks when I see that appear.
I've never been kicked but I just got so annoyed when you reach the end only for the healer or tank to just leave. Sometimes with no explanation. Or someone who starts by switching on their stealth so they can sneak past all the mobs leaving everyone else behind or after a battle, running back just before the enemies respawn behind them leaving everyone else trapped. Or gets in a huff cos someone got spotted by a mob because they didn't quite jump over the side of the balcony or stairs while pushed up against the wall exactly. Even during battles, Ive turned round and theyve already been running to the next part, leaving people behind. And needing on every bit of equipment.
I did do a FP recently just for a change, just stuck on group finder and played the first thing it gave me. It took over 4 hrs. Mostly waiting for new players to be added to the group cos someone just got up and left . But battled on to the end. (I think I was the only original member in the end). I didnt do anything wrong (AFAIK) but a tank left cos he died against a boss, healer not healing the tank, the other left cos someone got spotted by a Mob, got bored waiting for a new player, etc.. Although Im pleased I battled through it in the end its not something Id enjoy doing again. Most of the time I was trying to calm people down and finish.
Some people just cant seem to work as a team. Its supposed to be a team game. Through thick and thin. Dont get annoyed just complete the mission. Some people seem to freak out at the littlest things.
But I have given them a try again. And things have gotten smoother (Maybe cos Im not a newbie). It helps just to speak up. Best just to say at the very beginning. "Has anyone done this before?" (at least you wont waste your time if you get kicked or someone leaves.) Say is there a strategy for this boss?
When I had trouble I read that just going with people in their guild, or through friends found on previous. Can always ask people in your guild if theyd join you as at least you'll find someone who hopefully would get you through them. (Or create a friendlist of people who havent left you on a FP) Or hopefully wont kick up a stink if someone messes up.
Ahem.. Although I havent tried it myself...(member of a guild and never played with any of them... and my friends list is empty ) I must remember to try that rather than sitting in a group finder queue....