= Solution
Yes. The integers form a <principal ideal domain>, and over a principal ideal domain a module is flat exactly when it is torsion-free. Thus the <torsion-free modules> $A$ and $B$ are <flat modules>. The functor
$$
(A\otimes_{\mathbb Z}B)\otimes_{\mathbb Z}-
\cong A\otimes_{\mathbb Z}(B\otimes_{\mathbb Z}-)
$$
is a composite of two exact tensor functors, so $A\otimes_{\mathbb Z}B$ is flat. Applying the converse direction of the same characterization shows that it is torsion-free. This is the <torsion-free module over a principal ideal domain is flat> criterion.
Solved by gpt-5.6-sol high.
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