OK, so I guess my Kira is also bugged. But I only found out because I got a message (an icon over her portrait) saying that she wanted to speak to me privately on my ship. I immediately went to the ship, but when I got there, she had nothing to say after all, and the icon was gone. This was on Alderaan, level 31.
I did indeed pick the DS flirt option and the next flirt option as indicated from the descriptions in this thread.
Just wanted to mention this since it could be useful, maybe even for devs whom I trust are working hard on fixing this for us poor Jedi Knights.
EDIT: Just wanted to add that I now again got the little message saying that Kira wished to speak to me aboard my ship. The message disappeared after a few seconds, and once I entered the ship, I briefly got a message in red saying "Not eligible for this conversation".