Still, in the legion/regimental histories, I didn't find any reference to colours or standards actually carried. However, if something is not mentioned, it doesn't mean it is not there ...
The only one who had the right to give a flag to the legion, was the Russian Emperor, I presume ? Probably,the latter would have hesitated to give colours to a unit formed from foreign prisoners and yet without any battle records.
Of course, even if no official colours were issued, this doesn't rule out that "private" colours were made and carried.
I found Arndt's "Zwei Worte" of 1813. On p. 26, he mentions that the legion has been taken into British pay (in fact, the contract with England of 6th July 1813 laid down that the Hanoverian government was to pay for the legion), thus his text dates from the second half of 1813.
Arndt states:
Die Teutsche Legion hat ein Zeichen [...] In ihren [...] Fahnen sieht man den heiligen Georg [...]
Translated: The German legion has got a symbol ... in its ... flags [plural!] St. George is seen ...
If this is not poetical licence, it is a clear statement that these flags were actually carried.
However, in 1813, Arndt was staying in Berlin, so he might have described the legion from memory and from the plans he knew from the winter 1812/13, without knowing whether they were actually put into practice. His text mainly deals with the origin of the idea of forming the legion and what it was meant to be, no organisational details are given.
Oli