Very interesting!

"Chicken," probably a much shortened and revised version, or a different song, is found at www.kididdles.com, including a spelling verse:

"C" is for the little chick,
"H" for the momma hen
"I" cause I love that bird
"C" for the cluck, cluck
"K" for the kackle, kackle
"E" and the little "n"
C-H-I-C-K-E-N
That's the way to spell chicken
That's my friend, the chicken.

I think there are others, but I don't have time to look for them at the moment.