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?
Most groups I have found, if you let them know ahead of time that you've never read the dialogue/first time in that FP or Ops and you want to see it, not spacebar in a rush they will be fine with it. A few people might not, but usually people don't mind.
So just let people know ahead of time you won't be hitting space bar if people don't mind that, and all should be well.