I don't think that Baba gains his redemption in the novel. He tries to by building the orphanage, by treating Hassan extremely well while he and Ali still live with Baba and Amir, and by finally accepting Amir's writing at the end of his life. However, he never tells the truth to Amir or Hassan about his fathering Hassan. By taking that information to his grave, he keeps Amir from perhaps being able to save Hassan and Sohrab; for if Amir knew that Hassan was his half brother even just a couple of years before Rahim Khan breaks the news to him, he might have tried to make things right with Hassan. Baba never, as far as the author implies, tries to rescue Hassan and Ali from Afghanistan even though he obviously followed political events in the country and must have known that the situation there was grave.
In a sense, Amir's own redemption is partially for Baba, but then one must ask if one person can redeem another.