= Solution
For the standard symplectic form, $D_f=\sum_a(f_{p_a}\partial_{q^a}-f_{q^a}\partial_{p_a})$; a transformation is canonical when it preserves the symplectic form, equivalently Poisson brackets. The Jacobi identity gives $[D_f,D_g]=D_{\{f,g\}}$ with the stated convention. For $Z^A=e^{-sD_f}z^A$, differentiate $\{Z^A,Z^B\}$ in $s$; Jacobi makes the <derivative> the Lie transport of the bracket, preserving the canonical constant brackets at $s=0$. Hence every map in the one-parameter flow is canonical.
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