[9][10][11][12] In 2016, Kirkwood joined the inaugural Formula 4 United States Championship with Primus Racing, which saw him claim a win at Mid-Ohio and finish third in the standings overall.

[14] After competing with them in pre-season testing at NOLA, Kirkwood returned to the championship the following year, switching to newcomers Cape Motorsports.

[15][16] He achieved nine victories, including back-to-back hat-tricks at Indianapolis and Motorsport Park, wrapping up the title in the Formula One supporting season finale at the Circuit of the Americas.

[21] The season saw Kirkwood claim fifteen of the seventeen race victories on offer and seal his third consecutive championship at NOLA with a round to spare.

[22][23] The following year, Kirkwood made a one-off appearance with RP Motorsport in the season finale of the Euroformula Open Championship at Monza, which saw him take a best-placed finish of sixth in race two.

[26] In December 2016, Kirkwood partook in the Mazda Road to Indy Shootout, but lost out on the scholarship to Askew.

[37] The following month, Andretti confirmed Kirkwood would race with them for the 2020 season, only for that year's running of the championship to be canceled due to the COVID-19 pandemic.

As part of winning the Indy Lights championship, Kirkwood was guaranteed to compete in three IndyCar races in 2022, including the 2022 Indianapolis 500.