Wynne made his professional debut in 2016 with the Birmingham-Bloomfield Beavers of the United Shore Professional Baseball League, an independent baseball league. In 17 games (10 starts), he logged a 5–4 record and 3.08 ERA with 55 strikeouts across 61+1⁄3 innings of work. The following year, Wynne made 16 appearances (15 starts) and registered an 8–4 record and 3.30 ERA with 90 strikeouts in 95+1⁄3 innings pitched.[2]
Evansville Otters
On January 29, 2018, Wynne signed with the Evansville Otters of the independent Frontier League.[3] In 23 games (19 starts) for Evansville, Wynne pitched to a 9–9 record and 3.55 ERA with 114 strikeouts across 134+1⁄3 innings of work. He made 7 starts for the team in 2019, going 5–2 with a 3.42 ERA and 47 strikeouts in 50.0 innings pitched.[4]
Cincinnati Reds
On June 18, 2019, Wynne signed a minor league contract with the Cincinnati Reds organization. In his second game for the rookie–level Greeneville Reds, he recorded 17 strikeouts.[5] He made 16 appearances split between the rookie–level Arizona League Reds, rookie–level Greeneville, and Single–A Dayton Dragons, logging a combined 5–3 record and 3.34 ERA with 69 strikeouts in 67+1⁄3 innings of work.[6] Wynne did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[7]
In 2021, Wynne spent the season with the Double–A Chattanooga Lookouts. In 25 games (14 starts), he worked to an 8–4 record and 4.94 ERA with 67 strikeouts and 1 save across 89+1⁄3 innings of work.[8] He was promoted to the Triple–A Louisville Bats, pitching in 26 games (22 starts) and posting a 6–11 record and 4.75 ERA with 85 strikeouts in 132+2⁄3 innings pitched.[9]
He returned to Triple–A Louisville to begin the 2023 season. On June 25, 2023, Wynne was selected to the 40-man roster and promoted to the major leagues for the first time.[10] Wynne lost his major league debut that same day, pitching 2+1⁄3 innings with three hits and one walk allowed in a loss against the Atlanta Braves.[11] On June 26, Wynne was designated for assignment by Cincinnati following the promotion of Jake Wong.[12] He cleared waivers and was sent outright to the Triple–A Louisville Bats on June 28.[13]