Miles Thompson was drafted in the third round, 20th overall, in the 2014 MLL Draft by the Rochester Rattlers. He was then traded to the Florida Launch and was on the active roster with them in their inaugural season. In 2015, the Launch selected Miles' brother Lyle first overall in the 2015 MLL Draft. The brothers' first game together was against the Ohio Machine.
Miles was drafted third overall in the 2014 NLL draft by the Minnesota Swarm. After his rookie season in Minnesota, the Swarm relocated to Georgia, becoming the Georgia Swarm. Thompson's younger brother Lyle was also drafted by the Swarm the next season, and older brother Jerome was acquired by the Swarm in 2016.
As a player for the Iroquois men's national lacrosse team in the 2014 World Lacrosse Championship, Miles helped the Iroquois Nationals place third, their best-ever result in international field lacrosse competition.