The mechanics of Knives can be quite confusing. The best way to think of it is as a weapon replacement. So you will get the global bonuses (like +% Str or +% Piercing Damage) from your weapon (or shield, as that is a weapon too) but you won't get weapon-specific benefits like flat damage, resistance reduction or ADCtH. So no Knives of Harrowing, unfortunately.
You will get weapon procs such as Study Prey from Mbuti's because these are, bizarrely, considered non-weapon specific. Iirc almost all spells (Squall, VO, Eruption, Distortion Wave, Poison Gas Bomb, etc) will proc Study Prey, the only exceptions I can remember are the +% Health Reduction spells Deathchill and Plague. These do not proc Study Prey.
Similarly, you will get artifact procs on Knives too - Might of Hephaestus, Tyrant's Fist and so on. However, you only get the proc once on a Flurry of Knives, not nine times (ie once for each Knife).
The key with Knives is just to stack as much off-hand (ie non-weapon/shield) flat damage as possible. So things like the piercing damage completion bonus of Set's Betrayal, the flat Cold damage of Ethereal Veil, elemental damage from rings of Lightning/Frost/Fire, etc, will all boost your Knife damage considerably.