One solution is to solo the flashpoint. This is easy for anything with a story mode below level 50. Perhaps it is easy for many of the level 50 flashpoints too (I saw the thread mentioning someone soloing D7 hardmode!).
I also have the option of running these with my wife (another player + NPC). That probably opens up more options.
Generally, when pugging I spacebar through everything as a courtesy to the folks who have been through the mission too many times to count.
What are your suggestions for getting to see the dialog without torturing fellow group members?
Maybe when you are forming the group ask them that you would like to see the diaglouge upfront and that way they know what you are looking for and you may find others that would like to do this as well.
Another solution if you are in a guild let your guild know you would ike to do this as well.