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I've heard that on a Kähler manifold $(M,g_0)$, if you evolve the metric $g$ by Ricci flow $\partial g_{ij}(t)/\partial t=-2R_{ij}$, and $g(0)=g_0$, then you always have $g(t)$ is a Kähler metric on $M$.

All the references I saw refer this fact to that the holonomy group of $(M,g(t))$ is preserved under Ricci flow, but I don't know how to prove it.

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I know it is not too much, but I can suggest Chow's "The Ricci Flow: an introduction". You can find it for download here: – matgaio Apr 30 '12 at 19:36
In the case $M$ is simply connected this should follow since the Holonomy group changes continously with $t$ and by the Berger Holonomy classification this means that it must be constant. – wspin Sep 5 '14 at 8:39

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