When you are on the booking page it will state the following;

If you are a Kew Member, please select the 'Kew Member tickets' option under your preferred entrance. Select your date/time and there will be a box to enter your membership number.

Kew members can find their unique membership number on a membership card or any email correspondence with us. It will start with M or W. Email membership@kew.org if you have lost your details. Members may purchase up to 14 tickets per household.

If you have any issues with your membership, please read here.