Heinrich, who starts for WSV Schmiedefeld, started ski jumping in 2001 as a child. A good nine years later he continuously improved his performance in junior competitions and won a competition in the German Cup for the first time in December 2010. In 2011 he became German youth champion before winning this title with the team a year later. In February 2012 Heinrich started internationally for the first time as part of the FIS Cup in Baiersbronn . Already in his first two international competitions he was among the best 20. In August of the same year he competed in the Alpine Cup for the first time in Einsiedeln , but lagged significantly behind the top placings. It wasn't until February 2013 that he achieved his first points in the Alpine Cup with 12th place in Kranj . In January and February 2014, he jumped into the top 10 three times in Predazzo and Kranj. A few days later he traveled to Brotterode with the B national team to take part in the ski jumping Continental Cup there . With the places 70 and 49, however, he could not get any points. At the end of winter 2012/13, Heinrich made it onto the podium for the first time in third place in Chaux-Neuve .
At the end of January 2015 Heinrich returned to Zakopane in the Continental Cup and won his first 13 Continental Cup points in both competitions as 25th and 24th. In the end, he finished 106th in the winter and 145th place in the overall Continental Cup.
In the summer he started again in Wisła as part of the Continental Cup, but narrowly missed the points. In Kuopio, however, he finished 17th among the top 20. After two top 10 placements at the FIS Cup in Szczyrk , he traveled to the Ski Jumping Grand Prix in Almaty , where he also achieved a 27th and 25th place Was able to win points straight away. However, it remained his only starts in the Grand Prix, which brought him a 76th place in the end.
For the winter of 2015/16, after poor COC results in Klingenthal in October , Heinrich did not make the A or B squad again, but continued to jump in the FIS Cup. Only in Brotterode was it used again in the Continental Cup and surprised with a third place and thus his first podium finish in this series.