Is it common in the English language for "dragon" to be a metaphor for "defeat"?
No; it's just a very confusing metaphor here. 'Scaly' unquestionably implies a 'dragon'; and 'scaly dragon' suggests how unpleasant it all was for the Germans.Unfortunately the notion of the dragon bringing with it on its scaly wings thimgs which the defeated force has to accept suggests that the dragon is not defeat, but the agent of defeat (that is the victor); and in legend the dragon is always the bad guy who loses - dragons are fearsome enemies , but ultimately suffer defeat.
Possibly the metaphor of defeat as a dragon could be justified in itself (defeat is the cause of unwelcome happenings, as is a dragon), but in this context it results in a confusion of ideas; it would in any case be very far from a 'common' metaphor - in fact, it's probably a unique use.
EDIT We think of dragons when we read 'scaly' because 'scaly' has (from the nineteenth century) become a word which is almost automatically used to describe dragons; however, I can't actually recall any instances of their wings being described as scaly (of course, some creatures, like butterflies, do have scaly wings, but butterflies don't do much harm). Maybe Churchill re-imagined the dragon. In fact, whilst 'scaly' seems to have come into the language about 1300, a brief search doesn't turn up any instances of 'scaly dragons', let alone scaly wings, before about 1800, when 'scaly dragon' becomes the standard translation for the 'squamosus draco' (one of the forms assumed by Proteus) of Virgil's fourth
Georgic . I dare say many people are better informed about the history and iconography of the dragon - these are just tentative comments.