This should work.
model
{
for (i in 1:N) {
y[i]~dbin(p[i],1)
p[i]<-1/pow((exp(-beta0-beta1*x[i])+1),lambda)
}
beta1~dnorm(0,1)
beta0~dnorm(0,1)
lambda~dgamma(2,1)
}
list(y=c(1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0),
x=c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23),
N=23)
#Inits
list(beta1=1,beta0=0,lambda=1)