The answer to your question is in the second half of the following. . .
Can I track military aircraft? What about presidential movements in Air Force One? (Back to top)
FlightAware does not track military aircraft and presidential movement flights (e.g., Air Force One, Marine One, etc.) are operated by the US military.
http://flightaware.com/about/faq.rvt#military
Can I block my aircraft on FlightAware? (Back to top)
Yes, there are two ways to accomplish this:
FlightAware Selective (Un)blocking
Enroll in FlightAware's selective unblocking service for a tail number that is not already blocked.*
FlightAware can process your request with next-day service and will block your operations from the general public. Your FlightAware account(s) will continue to be able to securely view and track your aircraft. FlightAware will complete the paperwork necessary for blocking your aircraft on other flight tracking services and will provide you with everything you need to accomplish the block.
Blocking request through NBAA BARR
The NBAA (National Business Aviation Association) operates and maintains the BARR (Blocked Aircraft Registration Request) in conjunction with the FAA. This service is free although it may take 30-45 days to take effect and will not allow your user account to track your aircraft on FlightAware unless you subscribe to FlightAware's selective unblocking service.*
For us to submit your request, simply contact us to walk you through the process.
http://flightaware.com/about/faq.rvt#military