$B_ f$ is flat over $A$ for all topologically nilpotent $f \in A$,
$B_ g$ is flat over $A$ for all topologically nilpotent $g \in B$,
$B_\mathfrak q$ is flat over $A$ for all primes $\mathfrak q \subset B$ which do not contain an ideal of definition,
$B_\mathfrak q$ is flat over $A$ for every rig-closed prime $\mathfrak q \subset B$, and
add more here.
Proof. Follows from the definitions and Algebra, Lemma 10.39.18. $\square$
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