Kinman was drafted in the 25th round of the 2014 draft out of Bellevue University in Nebraska. The Braves sent the lefty to advanced rookie Danville. He pitched in 19 games, throwing 29 2/3 innings with a 2.43 ERA, 1.01 WHIP, and 6/43 BB/K. Needless to say, those numbers caught a lot of eyes in the Braves front office.
Kinman advanced quickly in 2015, starting in A-ball with Rome, but moving to high-A Carolina to start July before finishing in AA Mississippi from the end of July going forward. Overall, he pitched in 44 games, recording 18 saves over 51 2/3 innings.