Thank you for suggesting replying me possible flight connections.
＞Thank you for your reply suggesting possible flight connections
>Thank you for replying with possible flight suggestions
is grammatically wrong here
As you requested (The flight plan via Nagoya should be avoided because you need a separate ticket from Nagasaki to Nagoya), I will arrange your flights to Nagasaki from London as shown below. The reservation is not yet finalised. Please confirm that the plans below are satisfactory. If this is okay with you, I will complete the reservation.
A hotel accommodation has been reserved at Victoria Inn Nagasaki on 18th-19th November.