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.
I wanted to try myself in this new thing called yoga and I wanted to do good. I loved it and of course, got hooked. It became once a week, an hour and a half thing for me.
I don’t know how and why but I wanted to go to Goa, India to do my teacher training. Looking back now my gut must have told me to do it because my rational mind knew nothing about yoga not to mention teaching it. I was a single mom with a 10year old and even though I have looked up yoga schools, even though I have ordered the book they told me to, I couldn't go away for a month or 6 weeks. It just couldn’t work financially nor emotionally. I kinda did let go of it and went into childcare. I got myself educated and became a qualified Montessori teacher. For 7 years I was working with children.