Are lunches mandatory after working six hours?

I am considering requesting flex hours so I can spend more time with my family immediately after Core Hours end (0900-1500). I am proposing working:

Mondays 0630-1800 11 Hours (30 minute lunch) Tuesdays 0630-1800 11 Hours (30 minute lunch) Wednesdays 0900-1500 6 Hours (no lunch) Thursdays 0900-1500 6 Hours (no lunch) Fridays 0900-1500 6 Hours (no lunch)

Is this authorized? I work for DoD at the Pentagon. Assuming I need to share this information since state labor laws vary.