We have a business customer wanting to offer a flexible spending account to their employees. Is the amount the individual employee puts into the account insured by the FDIC? If so, is it the bank's responsibility to maintain the list of employees & balances or can the bank rely on the business'es records? any advice would be appreciated.

https://edie.fdic.gov/fdic_info.html#11f

There is a toll-free number for contacting the FDIC. Since giving incorrect advice on insurance coverage could make a person liable in the event of a loss, I'd recommend that you ask your question directly to them.

Without going through a qualified custodian? Employers do not normally manage these funds.