You basically want to do a left outer join. The way you currently are using the DefaultIfEmpty method is that if the entire list is empty you provide a single default entry.
You should join with PassengerDetails
and for each passenger details list call the default if empty. This is the equivalent of a left outer join and it goes a little something like this:
var data = from fd in FlightDetails
join pd in PassengersDetails on fd.Flightno equals pd.FlightNo into joinedT
from pd in joinedT.DefaultIfEmpty()
select new {
nr = fd.Flightno,
name = fd.FlightName,
passengerId = pd == null ? String.Empty : pd.PassengerId,
passengerType = pd == null ? String.Empty : pd.PassengerType
}