Hynčicová started in Horni Misecky in December 2010 for the first time in the Slavic Cup and finished 25th over 5 km classic and 10 km freestyle. At the European Youth Olympic Winter Festival 2011 in Liberec , she achieved 30th place in sprint, 28th place over 7.5 km classic and 22nd place over 5 km freestyle. The following year she came in at the Winter Youth Olympic Games in Innsbruck on the 30th place over 5 km classic, on the 12th place in the mixed relay, on the tenth place in the sprint. Her best placings at the Junior World Championships 2013 in Liberec were 37th place over 5 km freestyle and ninth place with the relay. In the 2013/14 season she reached the Slavic Cup with three top ten finishes, including second place in the sprint in Nové Město , ninth overall. In January 2014 she completed her first World Cup race in Nové Město , which she finished in 45th place in the sprint. Her best results at the 2014 Junior World Championships in Fiemme Valley were ninth place in the sprint and eighth place in the relay. At the U23 World Championships in 2016 in Râşnov , she finished 32nd place over 10 km classic, 28th place in sprint and 21st place over 10 km freestyle. The following year she ran at the U23 World Championships in Soldier Hollow to 22nd place in the skiathlon , 20th place in the sprint and 17th place over 10 km freestyle. Her best result at the 2018 Winter Olympics in Pyeongchang was 39th place in the 30 km mass start race.