R1 is advancing on the pitch from first base and F6 drops to a knee while taking the throw from F2, partially blocking the inside edge of the base. R1 slides to the inside edge of the base, contacts F6’s knee and is tagged out. Is this Obstruction on F6?

No This is Legal .  If the runner is given a part of the Bag/Home Plate to access, it is Legal to defend that base.