"don't think it matters do you really ???...
Well it does matter a little. If you see the locomotive the nameplates clearly say "Flying Scotsman". Similarly many locomotives are not prefixed by "The". It does seem to flow better, though if you say "I saw the Flying Scotsman today" than if you said "I saw Flying Scotsman today". But this seems to be one of the few instances where that might be so. As roseandily says. it would not seem quite so flowing if applied to other examples. Maybe it's because of te loco's fame.
There are a very few locomotives where "The" included properly in the name. I can think of a few steam locos offhand. Two are LNER Class V2s, both with tidy names: No 60809 "The Snapper, The East Yorkshire Regiment, The Duke of York's Own" and No 60835 "The Green Howard, Alexandra, Princess of Wales's Own Yorkshire Regiment". Others include BR Standard "Britannia" class No 70048 "The Territorial Army 1908-1958". A couple of "Standard Arthurs" were named "The Green Night" and "The Red Knight". A few of the 22 "Deltic" (Class 55) Diesel locomotives also spring to mind: "The Kings Own Yorkshire Light Infantry", "The Green Howards", The Duke of Wellington's Regiment" and "The Black Watch" are those I can think of.
"...there is only one after all"
Not strictly true. Although there is only one loco bearing the name there are three "Flying Scotsmen". As well as the loco there is the train (For many years the 10:00am Kings Cross to Edinburgh and the balancing down service). This was often pulled by th eloco of the same name but the service was shared amongst a number of "Top Link" locos and also by Deltic locos after steam was replaced. There is also the Route of the Flying Scotsman which is currently run by Virgin East coast trains.
I really must try to get out more but I'm rehearsing for my part as "The Fat Controller in "Thomas The Tank Engine - The Movie"