Kraus was born in Stratford, Wisconsin, where his father Mark raced super late models in the 2000s. Kyle began in go-karts, winning the GSR Kartway championship in 2012 and 2013 and the State Park Speedway bandolero championship in 2013 and 2014. He subsequently moved into super late models and midwest trucks.
In 2015, at just thirteen years old, Kraus became the youngest driver to win a feature at Rockford Speedway in the American Ethanol SuperTruck Series. He also won the Midwest Truck Series championship that year. In 2016, he entered the ARCA Midwest Tour, finishing fourth in the standings and surpassing Matt Kenseth as the youngest driver to win a race in that series.
Kraus joined Bill McAnally Racing for the 2017 NASCAR K&N Pro Series West season in the No. 19 Toyota Camry, and immediately showed promise. He won his first career race at Kern County Raceway Park that season, beating teammate and series champion Todd Gilliland, and earned the K&N West Rookie of the Year award.
His 2018 season was even more productive. He won multiple races across the K&N West, including victories at Kern County, Douglas County Speedway, and in a combination race at Gateway, and was named to the 2018 NASCAR Next class, which identifies top prospects in the sport.
In 2019, Kraus ran for the K&N West championship while also contesting K&N East races. Notable performances included winning both races in the Tucson Speedway doubleheader, leading all 100 laps in one event, and winning at Douglas County Speedway, Meridian Speedway, and Kern County. He clinched the K&N West championship simply by starting the final race at ISM Raceway, completing a dominant title defense.
In January 2020, Bill McAnally Racing announced the formation of McAnally-Hilgemann Racing in partnership with businessman Bill Hilgemann to run Kraus full-time in the No. 19 Tundra. He opened the 2020 season at Daytona with a career-best fourth-place finish. At Darlington, Kraus came within reach of his first career win, finishing second to Ben Rhodes in an overtime finish.
He continued with the team through 2021 and 2022 before being replaced by Christian Eckes for 2023.
After losing his truck ride, Kraus pivoted to a part-time Xfinity Series schedule in 2023 with Kaulig Racing, driving their No. 10. He also filled in for A.J. Allmendinger in Cup Series practice and qualifying at Richmond that year due to a scheduling conflict, an opportunity that arose from his role as Kaulig's simulator driver.
In February 2024, Kaulig Racing announced Kraus would drive the No. 16 part-time in the Cup Series, with his first start at Las Vegas Motor Speedway.
In 2025, Kraus drove the No. 44 Chevrolet for NY Racing Team in select Cup events, starting with the Coca-Cola 600, where he started 37th and finished 32nd. At the Cook Out Southern 500, his race ended prematurely after the car caught fire.
Kraus graduated from Stratford High School in 2020, where he was also a member of the wrestling team. He missed his graduation ceremony — rescheduled to July due to COVID-19 — to race in the Truck Series race at Kansas that day. After graduating, he relocated from Wisconsin to Charlotte, North Carolina, where most NASCAR teams are based.