We investigate the chirality of phonon modes in twisted bilayer
WSe
2
and demonstrate distinct chiral behavior of the
K
/
K
′
valley phonons for twist angles close to
0
∘
and close to
60
∘
. In particular, multiple chiral nondegenerate
K
/
K
′
valley phonons are found for twist angles near
60
∘
whereas no nondegenerate chiral modes are found for twist angles close to
0
∘
. Moreover, we discover two sets of emergent chiral valley modes that originate from an inversion symmetry breaking at the moiré scale and find similar modes in moiré patterns of strain-engineered bilayers
WSe
2
and
MoSe
2
/
WSe
2
heterostructures. At the energy gap between acoustic and optical modes, the formation of flat phonon bands for a broad range of twist angles is observed in twisted bilayer
WSe
2
. Our findings are relevant for understanding electron-phonon and exciton-phonon scattering in moiré materials and also for the design of phononic analogues of flat band electrons.