If you have two nouns modifying one another, such as lliw baner, the first one is automatically definite: "the colour of a flag".
Here, this happens twice: baner Cymru is "the flag of Wales", definite because it is this kind of noun-noun construction, and then lliw baner Cymru which is "the colour of the flag of Wales", which is again definite.
So there is no need for an y in the Welsh, nor is one possible.
It's a bit like things such as "that stone" or "my house" which are automatically definite in English -- you cannot say "the that stone" or "the my house". (Unlike, say, in Italian or Greek.)
What is possible is to have y before the second noun of such a construction; thus, for example, pen bryn "the top of a hill; a hilltop" versus pen y bryn "the top of the hill".