If you are eligible for command or non-command sponsored status then you can "try" to get a seat on the same flight your sponsor is booked on but there are no guarantees. You are on your own as an unaccompanied dependent and you must abide by all the rules for unaccompanied dependent travel. You may get to your sponsor's TDY destination on the same plane but there's no guarantee you'll return on the same plane as your sponsor (i.e. you may get stranded at the TDY location).
Can I travel Space-A on the same plane with my sponsor when he/she is going TDY?