Born in Cayenne, French Guiana, Inglis was a big soccer fan, but as his cousins played streetball, he first began playing basketball at age nine before moving to Paris as a teenager. Several years later, he recalled his move to Paris saying, "I was by myself. I left French Guyana when I was 14 years old. My family was far and I had to play basketball. It was cold, it was tough. I was family-sick, homesick. But I really wanted to make it, so that’s why I kept going."
Inglis grew up playing with INSEP, a French training institute for excellence in sports. The school had been previously attended by several promising NBA players such as Tony Parker, Boris Diaw and Ronny Turiaf. During his time with INSEP, he participated in two Nike International Junior Tournaments.
In association with INSEP, Inglis played for Centre Fédéral de Basketball of the NM1 (the third level professional league in France) from 2010 to 2013. While mostly playing for the U21 team in 2010–11, he did manage two games for Centre Fédéral, averaging three points and three rebounds per game. In 2011–12, he played 28 games, averaging 5.9 points and 3.4 rebounds per game.
On October 6, 2012, Inglis recorded 16 points, 11 rebounds and 6 assists against Cognac Charente Basketball and scored a season-high 31 points on November 10, 2012 against ADA Blois Basket, also adding on with nine total rebounds. The team would still lose the game by over 20 points. In 2012–13, he averaged 15.6 points, 7.3 rebounds, 3.8 assists, 1.5 steals and 1.2 blocks per game.
Inglis returned to NIJT play on February 22, 2013 against the KK Cedevita junior team, with 17 points, 8 rebounds, and 8 assists. Inglis scored 30 points against the USK Future Stars, marking his career-high scoring record in the event. Due to his success through the competition, Inglis was named to the 2013 NIKE International Junior All-Tournament team. Other recipients of the award were Nikola Jokić, Vasilije Pusica, Nikola Rebić, and Dušan Ristić.
On June 4, 2013, Inglis signed a three-year deal with Chorale Roanne Basket of the LNB Pro A. He debuted with the team on October 5, 2013, with 5 points and 2 rebounds against BCM Gravelines. Inglis also shot 2-of-3 from the field and made his only three-pointer attempted. His first double-digit scoring performance took place on November 2, 2013, when he logged 14 points, 7 rebounds, and 1 assist against JDA Dijon Basket. Inglis was finally allowed a start by head coach Luka Pavičević on December 14, 2013 against Orléans Loiret Basket, recording 3 points, 3 rebounds, and 3 assists. In 2013–14, he played 27 games, averaging 4.6 points, 3.6 rebounds and 1.0 assists per game. Following the season, Inglis commented on the experience of playing basketball in France, "My first year on a professional team was great. Even though my team dropped down to the second league, I had a good year. I played against good players. It was a great experience for me."
On June 26, 2014, Inglis was selected with the 31st overall pick in the 2014 NBA draft by the Milwaukee Bucks. Due to a broken foot he suffered during a pre-draft workout with the Oklahoma City Thunder, he sat out the 2014 NBA Summer League. After the event, Inglis said that Milwaukee would become "one of the destinations" for French Guianese immigrants in the United States. He was also compared with Kevin Séraphin after becoming just the second French Guianese player to be selected in the NBA draft. On August 26, 2014, he signed with the Bucks. Following a CT scan performed in mid-October, Inglis was ruled out for a further six weeks after it was revealed his fractured right foot was not healing properly. Inglis said, "I don't know if they messed up my surgery back in June, but something happened. I'm still not healthy." He was later ruled out for the rest of the 2014–15 season on January 5, 2015 after he underwent successful surgery on his ankle.
In July 2015, Inglis joined the Bucks for the 2015 NBA Summer League where he averaged 3.8 points and 2.5 rebounds in four games, ending what was a successful first outing for Inglis with the Bucks. He made his long-awaited debut for the Bucks in the team's season opener against the New York Knicks on October 28, recording 3 points and 4 rebounds in a 122–97 loss. On November 22, 2015, using the flexible assignment rule, the Bucks assigned Inglis to the Canton Charge, the D-League affiliate of the Cleveland Cavaliers. On December 5, he was recalled by the Bucks. On January 16, 2016, using the flexible assignment rule again, the Bucks assigned Inglis to the Westchester Knicks, the D-League affiliate of the New York Knicks. On February 29, he was recalled by the Bucks after averaging 9.9 points, 4.9 rebounds, 1.7 assists 1.4 steals and 21.4 minutes in 13 games for Westchester. On June 29, 2016, he was waived by the Bucks.
In July 2016, Inglis joined the New Orleans Pelicans for the 2016 NBA Summer League. On October 11, 2016, he signed with the New York Knicks. He was waived by the Knicks ten days later.
On October 31, 2016, Inglis was acquired by the Westchester Knicks of the NBA Development League as an affiliate player of the New York Knicks.
Inglis first played for the France junior national team at the 2010 FIBA Europe Under-16 Championship, averaging 4.5 points and 5.0 rebounds in 8 games as his team finished sixth place in the competition. Inglis returned to international play at the 2011 FIBA Europe Under-16 Championship, with per-game averages of 14.9 points, 7.8 rebounds, 1.4 assists and 1.6 blocks. He later appeared at the 2012 FIBA Under-17 World Championship, averaging 10.9 points, 7.7 rebounds and 2.4 assists. Inglis also played for France at the 2013 FIBA Europe Under-18 Championship where he averaged 11.8 points, 7.4 rebounds and 3.9 assists per game.