In reality the Fair Labor Standards Act doesn't apply to federal government employees, but it does apply to their equivalents in management and support at USPS. In reality the agencies make management and support personnel work under conditions approximating those that would apply if FLSA applied.
Here's where all the funny stories about government management come from ~ SCHEDULE C and APPOINTEES. That's where you get your pukes who never show up or spend all day in the toilet.
Every of the GS-15s I have known have had to fill out time cards, and could not log more than 40 hours per week on said card. Any time logged beyond 40 hours had to be approved as compensatory time. You cannot leave early to pick up your kid unless it is noted on your time card. The time you take for lunch is pre-negotiated and logged on your time card.
Now, I have only known GS-15s in the DoD. I do not know the policies of other organizations. But I was stunned how they treated one GS-15 who ran a multi-billion dollar weapons program. He was working his butt off, jetting off to DC to brief generals, then back to the office for a meeting with contractors, and if he left work 15 minutes early to pick up his kid from school his cell phone rang from the SES' secretary to accost him for his lack of integrity in his time card, and how important that time card is, and how they audit those time cards, etc.
The only white collar people I know who have to deal with this are lawyers with billable hours, and professional services employees who are billed hourly.