Stretching isn't something you can entirely outsource because it requires consistency. Once or twice a week of gymnastics or martial arts isn't going to cut it. They should be stretching 5 days a week if they are in any sport, and certain sports, like dance, figure skating, gymnastics, martial arts, etc require a longer stretching session each day than others.

I recommend you guys stretch together, as it's a nice bonding activity and good for you, too - I did this with my formerly inflexible daughter (2 years ago she couldn't touch her toes in a pike stretch and now she has her oversplits - and I have my splits for the first time). There are a lot of great online resources, like I love https://farfallastretchmethod.com/ and https://www.flex-abilities.com/, but since you have a boy, you might want to research some of the men on YouTube who have really great at-home mobility workouts. Boys generally want to stretch to a male instructor.

yoga? martial arts?

Swimming?

Both of my kids have stiff/inflexible body and poor eye body coordination. I put my 7 year old girl in gynmastic/tumbling classes, and she has fun with other girls. For my 10 year old boy, where can I put him? He is doing basketball and rock climbing once a week. He will not go to gynmastic or tumbling class. Where can I put him where all boys or mostly boys are? His body has been gaining some weight, especially around the upper body, and he is going through some awkward growing body change phases.