Green’s Dictionary of Slang

phoenix n.

[it ‘rises’]

the penis.

[UK]J. Cotgrave ‘A Rapture’ Wits Interpreter (1671) 230: The Phoenix too must build his nest.
[US] in Randolph & Legman Ozark Folksongs and Folklore (1992) I 393: Soon as I pulled old Phoenix out / She says, Ain’t it a beauty!