To determine which compound does not give oxygen on heating, we need to examine the decomposition reactions of each compound listed in the options. Let's analyze each option one by one:
Thus, based on the above analysis, $\ce{(NH_4)_2Cr_2O_7}$ is the compound that does not give oxygen gas on heating. The correct answer is: $\ce{(NH_4)_2Cr_2O_7}$.