2010-11: Simon Kindschi played 11 games at the U17 level in Switzerland as a 14-year-old and was one of the top scorers for the Davos U15 team. He had 1 assist in three regular season games for Davos in Elite Novizen play and scored 1 goal with 1 assist and 2 penalty minutes in six playoff games. He played two games with second level club Prattigau-Herrschaft in Top Novizen and scored 2 goals with 2 assists. Kindschi scored 11 goals with 13 assists and had 52 penalty minutes in 21 games with the Davos U15 team.
2011-12: Kindschi skated for Davos in the Elite Novizen and played for Switzerland's U16 team. He scored 6 goals with 12 assists and 32 penalty minutes in 32 regular season games. Davos lost to EHC Kloten in a first round series. Kindschi had 2 assists and 12 penalty minutes in four playoff games. In 16 games for Switzerland's U16 team he scored 3 goals with 6 assists and 12 penalty minutes.
2012-13: Kindschi played 27 games in Switzerland's U20 Junior A Elite League and played for Switzerland's U18 and U17 teams. He scored 2 goals with 2 assists and 10 penalty minutes in 26 regular season games and had no points nor penalties in one game for Davos during the playoffs. He also played 10 games for the Davos U17 team, including three games in the Elite Novizen playoffs, and scored 2 goals with 4 assists and 42 penalty minutes. Kindschi had no points with 2 penalty minutes in 10 games for Switzerland's U18 team. He was a team captain for the Swiss U17 team, scoring 1 goal with 2 assists and 2 penalty minutes in 10 games. He scored 1 goal with 1 assist and was +1 with 2 penalty minutes skating in three games as the squad captured a bronze medal at the Europe Youth Olympic Festival.
2013-14: Kindschi played in his first game in Switzerland's National A League and played for Davos in the Junior A Elite League. He played for Switzerland's U18 team in the 2013 Ivan Hlinka Memorial Tournament in August and played for the squad in the 2014 World Junior Championship. He had no points nor penalties in his only game with the Davos men's team. Kindschi scored 2 goals with 5 assists in 36 games for the Davos U20 team in the regular season and had no points with 2 penalty minutes in three playoff games as Davos was swept by SC Bern in the quarterfinals. Kindschi was ranked 93rd amongst European skaters in Central Scouting's final rankings prior to the 2014 NHL Draft.