[1] He signed and was assigned to the Idaho Falls Chukars, where he spent all of his first professional season, going 5–2 with a 3.58 ERA in 32+2⁄3 innings pitched.

In 2015, Stout played for the Arizona League Royals, Lexington Legends, Northwest Arkansas Naturals, and Idaho Falls, posting a combined 0–1 record and 3.15 ERA in 20 games between the four teams.

[8] On March 4, 2020, Stout re-signed with the Kansas City T-Bones of the American Association of Independent Professional Baseball.

On January 20, 2021, Stout signed with the Kansas City Monarchs of the American Association of Professional Baseball.

[11] On August 27, 2021, Stout re-signed with the Kansas City Monarchs of the American Association of Professional Baseball.

[12] On March 8, 2022, prior to the start of the American Association season, Stout's contract was purchased by the Chicago Cubs organization.

[16] On November 10, Stout was removed from the 40-man roster and sent outright to the Triple–A Indianapolis Indians; he elected free agency the same day.

[20] On July 19, 2023, Stout signed with the CTBC Brothers of the Chinese Professional Baseball League (CPBL).

Stout made 20 appearances (19 starts) for the Brothers in 2024, compiling a 10–5 record and 2.77 ERA with 109 strikeouts over 113+2⁄3 innings of work.

On August 28, 2024, Stout signed a contract with the Kia Tigers of the KBO League as an injury replacement for James Naile.