Thermite reaction beween zinc and iron(II, III) oxide
I'd check the Galvanic series.

$\ce{Fe(II)}$ and $\ce{Fe(III)}$ have an higher standard potential than $\ce{Zn}$ and therefore your reaction should take place.

I don't know how reactive it is but I had good experiences with also using $\ce{HCl}$. Use $\ce{Zn + HCl}$ to produce $\ce{H2}$ and heat $\ce{Fe2O3}$ in the presence of $\ce{H2}$ to produce $\ce{Fe}$ and $\ce{H2O}$.