You apply the same process, but your hypotheses are "bug is before/after this bisection point". Your "probability of evidence given hypothesis before/after" are where you incorporate your guess about the tests flakiness. Still works even if you don't have "true" numbers for the tests flakiness, just won't converge as quickly
When gathering more evidence, you'd use your new belief about which cookie bowl Fred has as P(H1)=0.6 and P(H2)=0.4