The first step in using nitrate spray to kill oak tree roots is to cut your stump as low to the ground as possible. You want to limit the amount of energy reserves available to the tree to send out more roots and shoots. Cut away as much of your stump as you can before turning to nitrates for decomposition.
Cutting grooves in to the top of your stump can help give fungi and bacteria a place to gain a foothold on the wood. This will also be helpful when it comes to applying nitrate spray. The further in to the stump you can get the nitrates, the less likely they are to be washed away during the first rainfall. Drill as many holes of varying size and depth in to the stump as you can.
Spray nitrates liberally on the stump and in the holes and grooves you have cut in to the wood. Until the stump begins to decompose, bacteria and fungi that would feed on the wood will be nitrogen deprived. Supplying nitrogen in the form of nitrate spray will help them gain a foothold on your stump and begin the decomposition process.
Do not focus only on the main stump when spraying nitrates. Trace the roots out away from the stump as far as you can and continue cutting grooves and drilling holes in the wood. Spray the roots liberally with nitrates and avoid hitting grass or other ornamentals, as too much nitrogen can be damaging to lawns and plants.