Flex spending accounts have to follow the IRS rules for deductible medical expenses. You'll have to get a diagnosis saying hair removal "is necessary to improve a deformity arising from, or directly related to, a congenital abnormality, a personal injury resulting from an accident or trauma, or a disfiguring disease."
I suspect that the administrator of your Flex Spending Account will be very conservative when interpreting the IRS regs because the IRS makes the final determination of the interpretation. In other words, I doubt they will allow a reimbursement for hair removal because if the FSA is audited, they risk penalties from the IRS if the IRS disagrees with their decision. I hope I'm wrong, but thought I should let you know the chances of getting it approved are low.
Here is the IRS regulation.
http://www.irs.gov/publications/p502/ar02.html#d0e2334 Cosmetic Surgery
Generally, you cannot include in medical expenses the amount you pay for unnecessary cosmetic surgery. This includes any procedure that is directed at improving the patient's appearance and does not meaningfully promote the proper function of the body or prevent or treat illness or disease. You generally cannot include in medical expenses the amount you pay for procedures such as face lifts, hair transplants, hair removal (electrolysis), and liposuction.
You can include in medical expenses the amount you pay for cosmetic surgery if it is necessary to improve a deformity arising from, or directly related to, a congenital abnormality, a personal injury resulting from an accident or trauma, or a disfiguring disease.
Example.
An individual undergoes surgery that removes a breast as part of treatment for cancer. She pays a surgeon to reconstruct the breast. The surgery to reconstruct the breast corrects a deformity directly related to the disease. The cost of the surgery is includible in her medical expenses.
Electrolysis or Hair Removal
See
Cosmetic Surgery, earlier.