2021–2022 At his first Florida High School 1A State Championships in the autumn of 2021, Winkler placed second in the 100-yard freestyle with a time of 44.00 seconds and second in the 200-yard freestyle with a time of 1:36.78. In March the following year, he became the fastest American 15-year-old swimmer in history in the
long course 100-meter freestyle with a time of 50.24 seconds at the 2022 Piranhas Senior Invitational in Florida. In April, at the
2022 USA Swimming International Team Trials held in
Greensboro, North Carolina, he placed fourth in the c-final of the 100-meter freestyle with a time of 49.95 seconds and 33rd in the 200-meter freestyle with a 1:52.05. The next month,
USA Swimming selected him to the 2022 Junior Pan Pacific Swimming Championships roster in the 100-meter freestyle based on his results at the International Team Trials.
2022 Junior Pan Pacific Championships Day one of four at the
2022 Junior Pan Pacific Swimming Championships, held in August and contested at
Veterans Memorial Aquatic Center in
Honolulu, Winkler placed fourth in the b-final of the 200-meter freestyle with a time of 1:50.81 after swimming a personal best time of 1:50.07 in the preliminary heats. On the second day, he placed second in the b-final of the 100-meter freestyle with a 50.12, after swimming a personal best time of 49.47 seconds in the preliminary heats, and contributed a split of 1:51.27 for the fourth leg of the 4×200-meter freestyle relay to help win the exhibition heat with a time of 7:22.66. In his first event of the evening session on day three, Winkler won the b-final of the 100-meter butterfly with a personal best time of 53.94 seconds. The following, and final, day, he tied fellow American Diggory Dillingham for the silver medal in the 50-meter freestyle with a personal best time of 22.50 seconds. In the 4×100-meter medley relay final, he and relay teammates Daniel Diehl (
backstroke),
Zhier Fan (
breaststroke), and Thomas Heilman (butterfly), won the gold medal with a Championships record time of 3:36.65. He contributed a split time of 49.18 seconds for the freestyle leg of the relay. He also won the state title in the 200-yard freestyle, in which he set a Florida high school record with a 1:34.18. At the
2022 U.S. Open Swimming Championships, held in November and December in Greensboro, North Carolina, Winkler tied for nineteenth-place in the 50-meter freestyle on day two with a time of 22.97 seconds, which qualified him for the c-final. He lowered his time to a 22.82 in the evening to win the c-final. The following day, he swam a 1:50.97 in the preliminary heats of the 200-meter freestyle to qualify for the b-final ranking eleventh across all preliminary heats. Improving his time in the evening finals session, he won the b-final with a time of 1:50.26, which was 2.88 seconds slower than a-final winner
Jake Mitchell. For his final event, the 100-meter freestyle on day four, he ranked seventh in the preliminary heats and qualified for the a-final with a time of 49.56 seconds. In the evening final, he achieved a sixth-place finish with a personal best time of 49.45 seconds.
2022 Winter Junior National Championships Later in December, at the 2022 Winter Junior US National Championships, Winkler finished in a personal best time of 19.70 seconds in the 50-yard freestyle to place fourth at the East edition of the meet. The following day, he placed second in the 200-yard freestyle with a personal best time of 1:33.36. In the morning preliminaries on the fourth and final day, he swam a personal best time and new boys 15–16 National Age Group record of 42.21 seconds in the 100-yard freestyle to qualify for the final ranking first, his time broke the record he set in the event less than one month earlier at 42.52 seconds. He won the event in the evening with a time of 42.22, which was one-hundredth of a second slower than his time in the morning.
2023 At the second stop of the 2023 TYR
Pro Swim Series in March in
Fort Lauderdale, Florida, Winkler started competition on the second day with a national age group record for the boys 15–16 age group in the 100-meter freestyle, finishing in a time of 48.81 seconds in the preliminaries and qualifying for the final ranking third. In the evening he finished in 49.11 seconds to place fourth, 0.83 seconds behind gold medalist
Dylan Carter. The following day, he placed second in the b-final of the 200-meter freestyle with a personal best time of 1:49.02. The fourth and final day, he placed sixth in the final of the 100-meter butterfly with a personal best time of 52.64 seconds. For his final event, he won the b-final of the 50-meter freestyle in a personal best time of 22.49 seconds, finishing two-hundredths of a second ahead of the second-quickest b-final finisher
Diogo Ribeiro of
Portugal. Fifteen days later, he lowered his personal best time and national age group record in the 100-yard freestyle for the boys 15–16 age group to a time of 41.96 seconds at the 2023 Florida Gold Coast Swimming Championships.
North Carolina State University Kaii enrolled at
North Carolina State University, beginning in the Fall of 2024, where he was managed by Head Coach
Braden Holloway. In his Senior High School year, he was ranked as the top male swim recruit from Florida and was rated fifteenth in the nation. ==2024 Paris Olympics==