I was also confused. 'Gift for' is what you should say. Otherwise it can seem like you have a painting that was gifted. 'I inherited a gift for painting from my dad' is OK.

It took me a while to understand what you were asking, but i finally got it :p You would/could say "I inherited my painting skills from my dad." or "My painting skills come from my dad." or "I'm gifted in painting because of my dad." any of those work in formal and informal settings.