To be fair, River flirted like breathing, she probably didn't even notice she was doing it nor when people did or didn't respond. Unless you were the Doctor, she was always attuned to if they flirted back it was a wonderful yardstick for where her relationship was with them.
"OH, well yes and no. It's..." She considered how to explain, if she even wanted to explain. "It will be the end of something that isn't ready to end."
Her life. Her love. Her story. She doesn't know. She thinks the Doctor might know and that is why they keep putting it off.
"I feel a bit invincible because of I haven't see it, I know I do someday so I simply can't die until I do."