Killing moss on trees is a tricky proposition because any herbicide you apply to the moss is going to poison the oak tree as well. Consider carefully whether you even need to kill the moss first: mosses do not kill or damage oak trees, they simply coexist with them and use their structure for advantageous growth. Most tree owners’ major concern with moss on their trees is, simply, the fact that it's unattractive.
Apply a moss-killing product containing ferrous sulfate or ferrous ammonium sulfate, such as Moss-Out, Moss-Kil, Rid-Moss and others. Pay attention to safety precautions on the label, and wear gloves to keep the chemical off your skin.
Apply this according to the directions. Depending on the strength of the product, different timing and application may be needed. Do not leave it on the moss longer than recommended, as you don’t want it to affect the tree.
Re-apply if needed. Sometimes these products require more than one application. You should wait at least a day to see if the moss is dead or not; it should brown up and dry out if it is dying.
Rake off the dead moss. Use a plastic-tipped rake or a hand-raking tool, as for gardening, to avoid damaging the tree bark underneath. You can pick off remaining or tough bits by hand, too, if needed.
To prevent moss from coming back, make sure all the roots are dead. This means letting bleach soak into the bark where the moss was living. This is not good for the oak tree, but it will recover after a few years if you don’t overdo it. If you do this, just use a rag or sponge soaked in household bleach and work it into the bark. Limit the area you apply bleach to so that the tree is not poisoned too heavily.