LFG tab wouldn't be bad.
Otherwise just skip the flashpoint and do it at a different time. What's to say that people would even respond to you wanting to do the flashpoint even after an LFG tab is created? It's all based on people and what time they have.
I might be looking for a group on my server for just a regular heroic quest at one hour (probably 1pm) and no one even gives a ****. But when I come back like 3 hours later, everyone and their mom wants to do the quest and people begin asking around 10 minute intervals until maybe 2:30am.
The only problem with skipping flashpoints is that when you go back and do the quest when you're higher level you get something like 5XP for completing the quest when you're done. This may just be after you already ran said flashpoint, but if you're only gonna get 5XP for it, what's the point of making it a daily quest? Just to be able to do the bonus mission again?