Generally, you take revenge on someone, or for something - you don't take it from them. There are multiple ways of expressing this:
to take revenge (against somebody)
to seek revenge (against someone)
get revenge against someone
take revenge (on someone) (for something)
However, in the example you have provided:
One day my son will grow up and get my revenge from you.
...implies that the son is taking the father's revenge, which is not possible. Revenge is a personal thing - you can take it for yourself, or you can take it on behalf of somebody else, but you can't take somebody else's revenge. The closest alternatives to your sentence would probably be along the lines of:
One day my son will grow up and take/seek/get his revenge (from you).
One day my sone will grow up and revenge me. (correct, but not commonly used)
Another alternative available is the word avenge, which (in my opinion) is more suited to this scenario.
avenge and revenge both mean to seek or get vengeance. However, avenge specifically means to take vengeance or exact satisfaction for (a wrong) by punishing the wrongdoer, which is exactly what you describe.
...are two ways of expressing this, but it can be reworded in a number of fashions.