How do I install this knee brace to my pergola post?
Prior to drilling the "through-hole", mark the location on both sides and use a paddle-style wood boring bit slightly larger than the O.D. of your flat washer, to make a large flat-bottomed hole.

Make the holes no deeper than necessary to make the nut, washer, and bolt end sit flush (you would need a shorter bolt).

For more precise creation of a flat-bottomed hole you could also use a Forstner style drill bit, but they are significantly more expensive than a paddle-bit. It depends on how nice and clean you want the hole to be.