You can see here that it is (-1).
http://pdglive.lbl.gov/Rsummary.brl?nodein=S011&sub=Yr&return=MXXX020
Note that for mesons, parity only depends on the orbital angular momentum L as
P=(-1)^(L+1)
but since J=0 for K0, and the parity is negative, that implies that L=0 and s=0 are zero too, therefore they will be zero too for the K0 bar, and the parity will be also (-1).