I found an example of "Water-Flower" in an old book of African American play songs, Play Songs of The Deep South by Alotna Trent Johns {Washington, D.C.,The Associated Publishers, Inc, 1944}.

Here's that example and my comments:

Subject: RE: Children's Street Songs
From: Azizi - PM
Date: 05 Jan 05 - 06:35 PM

1st verse:
Water-flower, water-flower
growing up so tall
All the young ladies must surely, surely die
All except 'Lindy Watkins,
She is everywhere-
The white folks say, the white folks say,
Turn your back and tell your beau's name.

2nd verse:
Doctor, doctor, can you tell
What will make poor 'Lindy well?
She is sick and 'bout to die
That will make poor Johnnie cry.

3rd verse:
Marry marry, marry quick!
'Lindy, you are just love sick!

4th verse:
Johnnie is a ver' nice man,
Comes to the door with hat in hand,
Pulls off his gloves and shows his rings,
"Morrow is the wedding-day.

-snip-

"Water-flower" is described by Altona Trent Johns as a pantomine ring {cicle} game with one girl in the middle; a boy is said to act out the role of the doctor*. The "doctor" directs the boys who 'Lindy has named to come into the center of the ring and act out the role of "Johnnie"...

*This rhyme was composed and played before the Women's Liberation movement! This rhyme also was composed and played at a time when boys and girls older than pre-school ages played "singing games" together, and initiated that kind of play without adult urging.