There are multiple types of flexibility exercises. Where, when and how you utilize these methods is dependent on your goals and needs.
All stretching is not the same. Static (no movement, long holds) stretching and Dynamic Flexibility (constant movement, mimics or mirrors a movement in life or in fitness) are completely separate things.
Workout preparation/ warm-up will be built around dynamic flexibility. These movements are used to prepare your body for movement, increase core body temperature and blood flow, excite the nervous system and ignite dormant/inactive muscles.
A static stretch is useful for muscle recovery post workout to increase blood flow and the delivery of nutrients into muscles. It would also help to reset the nervous system and create a better balance between underused and overused muscles (agonist/antagonist) and/or during the day to reactivate dormant muscles and lengthen the shortened muscles usually caused by lifestyle/postural imbalances.
Foam rolling - is a type of flexibility exercise that focuses on releasing adhesions (knots) in the fascia (connective tissue that surrounds and protects muscles).
So, as you see, the warm-up that occurs during your metabolic session is dynamic in nature (arm circles, lateral lunges, hip circles, jump and jacks etc...) however, there is certainly a place for static stretching.