No, you do not need to be flexible to do yoga. However, what you need to be is to be patient. Stretching happens when you can fully relax your muscles (no forcing) and body/mind can best be relaxed when you breathe. In through your nose and out through your nose. Slowly and deeply. Consciously. Conscious breathing takes effort. It makes you connect with yourself. As you focus on your breath, the mind can't wander. No "shopping list", no "what I am going to cook tonight", and no "who is picking up the children tomorrow" type of conversations. Yoga will allow you to enjoy your own company and free yourself up.