In almost every case, no.
Expenses incurred merely to improve the taxpayer's general health are not reimbursable by an FSA when unrelated to a treatment plan for a specific illness or injury.
The term "medical care" is defined by Treas. Reg Section 1.213-1(e)(1)(i) to include expenditures incurred "for the purpose of affecting any structure or function of the body... primarily for and essential to medical care."
Health spa memberships and exercise programs, even when prescribed by a physician, are not reimbursable by a FSA, absent physician substantiation that the expense was primarily for or essential to specific medical care.