Do I need to be flexible to do Yoga?

In short NO!

Whether you can touch your toes or not does not have any bearing on you practising Yoga. There are many postures you can do that will improve, balance strength and flexibility. From laying down, sitting, kneeling, standing or on all fours. Its a journey, and it starts with a single first step. No gymnast began being perfectly flexible or strong and no musician knew how to play beautifully with out practice. Come to class and see where your starting point is and know with attending more sessions, self practise at home and time, you will be more flexible as well as calming the mind.