I was sent to a training and had to leave on Sunday in order to arrive at the training site on time. I claimed 8 hours because of the time we had to leave to be at the airport to check-in, flight time, and arrival time. When I returned to work I was informed that the 8 hours I claimed on Sunday did not count toward my 40 hour work week because it wasn't done during regular work hours. I was told I either had to come in and work Friday for 8 hours or take annual leave. Is this correct? legal?

If you did not travel during your regular working hours, for example 8-5, then no, the travel time is not compensable. And so far, the DOL has not extended the "travel time" to include travel to the airport, checking in, going through security, etc.

I'm assuming you're a nonexempt employee.

If you did not travel during your regular working hours, for example 8-5, then no, the travel time is not compensable. And so far, the DOL has not extended the "travel time" to include travel to the airport, checking in, going through security, etc.

I'm assuming you're a nonexempt employee.

You're correct I'm a nonexempt employee, but my flight was between 8-5 so can I claim the just the flight hours?

Yes, you can. That is compensable time under the FLSA regulations.
http://www.dol.gov/dol/allcfr/ESA/Title_29/Part_785/29CFR785.39.htm