which martial art peoples have more flexible body.

In China they start children at 5 years of age but a lot of the training they receive then is 'conditioning' or pre martial arts training. The kids learn coordination, agility, flexibility, speed and with all those exercises comes strength without weight training. Kids also learn discipline, focus, patience and that things are expected of them. They also learn that they are not perfect but perfection is something that can be achieved through hard work, and that they can not do whatever they want, that not everything they do is good and that they have to work on their character traits. All those things are not only pre requisites in martial art but also pre requisites in life.

In America kids have a great deal of difficulty understanding these concepts. Nothing is expected anymore, kids are great no matter what they do and if they don't want to try hard they are still great and get advanced in school. Math problems do no longer have to be correct as long as you can explain how you got to the wrong answer, spelling is not expected anymore because everybody else will adapt to whatever the kid is willing to give. You get the idea.

At about 8 years old a child can grasp basic techniques like kicks and punches but they still are struggling with coordination and their ever changing and growing bodies which constantly throws of their center of balance.

In the early teens is probably a good time to start learning the motion of striking techniques more seriously. Techniques like joint locks/joint manipulations and techniques that rely on pain compliance are usually not taught until the kids are 16 simply because the bones are still soft and the body is still growing and the constant twisting of joints and the amount of pressure applied to bones over a period of time can cause damage.

It is not so much at what age to teach martial arts as it is what aspect of martial arts to teach when. If you start a child young and teach them coordination, agility, flexibility and speed it will be a great benefit later when they do start learning actual techniques so it is not necessarily wasted time or a babysitting service as long as the parents know that their 5 year old will not be punching and kicking or defending himself at age 5 or 8 or even 10. Even though he might be able to imitate the motion he would have no concept of application nor would he have any detail of how to generate power nor would he have the mental judgement of when to use such techniques. To a pre teen a sibling who took away his toy car would be deserving of kicks and punches. Not the right way. With knowledge comes responsibility and if you give knowledge and ability too early the knowledge most likely will not be used correctly. Same reason why you don't let your pre teen drive your car even though mechanically they could, they simply do not have the judgement to do so safely.

It's all what you teach when.

Depends on how active the kid is. If the child is a playful and skinny one, it can join martial art at age of 4 ! But for an obessed one I think its around 6 or 7. The youngest black belt in karate in the world is just 5. I think shotokan karatekas have more flexible bodies.. ...

Just about any martial art that incorporates kicks will make you more flexible, but Taekwondo, Hapkido, Karate, Wushu, and Capoeira are some of the best in that regard. It also depends why you want to teach your kids; for something fun and flashy, Taekwondo, Wushu or Capoeira would be good; for sporting reasons Taekwondo or Judo is perfect and for self defense I'd recommend Hapkido or Wing Chun.

As for what age, I'd say you're never too old or too young. Just make sure you find a good school.

That depends on your child's attention span. At 4 to 6 their attention span is too short and it is more like a baby sitting service then a martial arts class

7 or 8 they have a decent attention span and can learn a lot more. This is the age I recommend

As for children black belts that is a joke a 5 year old is not the same as an 18 year old and has no business being a black belt they are not mentally the same which is bart of being a black belt. My dog is a better 23 degree black belt then any 5yr old

Capoeira sounds like what your asking for.

In capoeira your kids will learn hispanic dance/fighting that has many kicks and acrobatics. They will also learn to play instruments.

The art is really fun in itself, it derives from brazilian slaves. I have done it before, though I didn't really like the instructor just because of his personality.