What do Burning Tree South lot owners have an easement to use?

ANSWER FOUND IN BURNING TREE SOUTH COVENANTS:

H (c) Membership in Home Owners Association.
Any owner of any lot within said subdivision shall become a member of Burning Tree Area #4 Association, Inc. by purchasing a lot within said subdivision and memberships there shall thereafter be appurtenant to the ownership of said lot. One cannot be transferred without the other. Voting within Burning Tree Area #4 Association, Inc. will be on the basis of one vote per dwelling unit owned, and the assessment will be made on a “per dwelling unit” basis. Each and every lot owner shall have an easement to use the facilities of the Association of which said lot owner is a member, and of the Burning Tree Master Association, subject however, to the rules and regulations thereof. Membership in the Association shall be subject to assessments for the actual cost of maintenance, repair and upkeep shall be a lien upon any lot of any owner in said subdivision, for the unpaved areas of the Boulevard and facilities as designated on the overall developmental plans for Burning Tree. Annual  assessments for maintenance, repair, and upkeep shall be a lien upon any lot of any owner in said subdivision,and shall be subject to enforcement as provided in the By-Laws of the Association. The articles of incorporation, by-laws and rules and regulations may be examined at either the office of 61st and Memorial Development Corporation 9511 East 46th St., Tulsa, Oklahoma, or at the clubhouse office of the Association to be built in said subdivision.

WHAT THIS IS SAYING:  That lot owners become a member of the homeowners association, Burning Tree Area #4 Association, Inc. and they have an easement to use the facilities of both their association and the facilities of the Burning  Tree Master Association as long as they follow rules and regulations of each. Click to see Rules and Regulations  Burning Tree Master Association.

And as you can see, the Burning Tree South Certificate of Dedication was filed stating that there would be a clubhouse in the subdivision.