The oxidation state of chromium in the final product formed in the reaction between KI and acidified $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ solution is:

In the reaction between KI and acidified $K_2Cr_2O_7$, Cr in the dichromate ion exists in +6 oxidation state. Iodide ions are oxidized to $I_2$ while chromium is reduced. The reduction product is $Cr^{3+}$ ions, which form chromium(III) salts like $Cr_2(SO_4)_3$ or coordination complexes. Therefore, the oxidation state of chromium in the final product is +3.