The "six flat-ish sides" on your bullet are rifling-marks made by the gunbarrel's rifling grooves when the bullet got fired.
Almost all of the bullets from the 1800s which have a flat solid base were made for use in breechloading or cylinder-loading firearms. Because your fired bullet show 6 rifling-ridges, and its diameter is a bit larger than .50-inch, it was most probably fired sometime during the 1850s-through-1870s from a Sharps Rifle/Carbine.
However, your fired bullet does not have the shape of a Sharps bullet. We know with certainty that if a Sharps bullet wasn't available, other versions of bullets were used if they would fit into the Sharps Rifle/Carbine's breech. To give you a specific identification of your bullet, I'll need you to super-precisely measure its diameter with a Digital Caliper (which measures in 1/100th-of-an-inch increments). Also, it would be helpful to see additional well-focused closeup photos which show your bullet's grooved sides from several directions.