My son was in Basic Combat Training for 10 weeks and then started his Military job training (Jan.-May of 2021. Would he have been considered a student during this time?

Are you asking in regards to an education credit or the ability to claim your son as your dependent? 

For an education credit, no, that would not count, only an academy such as West Point would count. 

If asking about your son being your dependent, how old was he at the end of 2021? Did he attend school in 2021 (besides Military) and if so, how many months? For example, was he in High School from January till May 2021?