Jack asked:

What is a logical relationship between Nietzsche's "Will to Power" and altruistic inclinations?

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It follows from the nature of the will to power that altruism can only be understood as self-interested.
The will to power is egoistic and there is no such thing as the disinterested act, i.e. an act simply for
others. Nietzsche allows there are acts we describe as altruistic, but on his view they are not done for
the other but for the self. Such acts only seem altruistic because we deceive ourselves.

Logically, altruism as self-interested or prudent altruism, is inferred from the nature of the will as
seeking power and freedom. If we act badly towards others, they will not allow us to dominate them
so easily. They may turn against us. This will interfere with our will to dominate as well as our
freedom because the way others treat us will not be with the respect and subjugation that we want.

Rachel Browne