To teach a children's yoga class you must first have completed a children's (or teen's) teacher training qualification, specifically covering the age ranges you are looking to teach. Alternatively, your original training qualification must have included modalities of children’s yoga.
You must have written permission from the children's parent or guardian and you should keep a record of this for a minimum of 7 years after the student has reached the age of 18.
Depending on the age of your students, the requirements of your venue and whether or not the children's parents or guardians will be present you may need to have a DBS check (or similar) in place.
See also:
Can you organise a DBS check