Ceolas lists "Cluck Old Hen" in the repertory of Fiddlin' Cowan Powers, recorded by Edison in 1925.

Talley, "Negro Folk Rhymes," expanded edition of 1992 (original 1922) has a rhyme called "The Old Hen Cackled," which belongs with Carson's recording of 1923 (see Stewie, above). #69, p. 44.
Can't find any rhymes suggestive of "Cluck Old Hen" in this edition of Talley. Meade probably referred to the first edition of 1933. Talley does not date or indicate sources for the rhymes; perhaps these data are in his manuscript notes.

THE OLD HEN CACKLED

The ole hen she cackled,
An' stayed down in de bo'n.
She git fat an' sassy
A-eatin' up de co'n.

De ole hen she cackled,
Git great long yaller laigs.
She swaller down de oats,
But I don't git no aigs.

De ole hen she cackled,
She cackled in the lot.
De nex' time she cackled.
She cackled in de pot.