The answer is **yes**.

In fact, there is the following result, see 
Banica-Stanasila, *Algebraic methods in the global theory of Complex Spaces*, Theorem 2.12 p. 180.

>**Theorem.**
Let $f \colon X \to Y$ be a morphism of complex spaces and let $\mathscr{F}$ be a coherent analytic sheaf on $X$, which is flat with respect to $f$. Then the restriction of $f$ to supp($\mathscr{F}$) is an open map.

In particular, every flat morphism is open.