Are some people born with flexibility? Probably. But genetic predisposition is not the only factor that influences one’s flexibility.
Gender, body type, age, prior injury, and sedentarism all play a role in impacting level of flexibility. The most important factor for flexibility, however, is the use of the joint itself.
In other words, the more often a joint is exercised and brought through its normal range of motion, chances are it will be more flexible.