The Library of Congress has a surprising number of songs with "flirt" in the title. Here's one:

THE LITTLE FLIRT.
Words and music by Andy Hughes.
Philadelphia: Lee & Walker, 1870.

1. Of all the girls that ever was, and all that e'er may be,
There is none I think so charming as the girl that looked at me.
Her eyes they shone like diamonds bright and her curls they were jet black,
And my heart is almost breaking. How I wish she would come back!

CHORUS: O how I wish that I could see this little dear again!
Like cupid's dart she pierc'd my heart and almost turn'd my brain.

2. At Schutzen Park I went one day to see my little dear,
And when she spoke, it seem'd to me that we had met somewhere;
But when I ask'd her where it was, she laugh'd at me so sweet,
And then she said that she'd tell me the next time we should meet.

3. So to her house I went next day, this little dear to see,
And ask her if she'd kept the promise she had given to me.
Then with a smile upon her face, said, "Yes, my dearest Fred,
'Twas up at my papa's house, the night that I was wed."

4. Oh, then with a cruel laugh she offer'd me a chair,
While she would just step out and see if her dear Gus was near,
So that we three could laugh and chat at my flirting scene with her,
But this was rather hard on Fred, so I left without demur.