"I like Dublin's flag's colour."
Translation:Dw i'n hoffi lliw baner Dulyn.
Welsh doesn't express possession in the same way as English. Think of it as "I like [the] colour [of the] flag [of] Dublin". It's like the genitive case in Irish or Russian, but without actually inflecting the words.
o (from) sometimes does the duty of English "of", but context usually does fine by itself.
There is no "a flag of Dublin" or "a colour of the flag", so the words can only be definite ("the flag of Dublin", "the colour of the flag"). Where you can tell from context that something is definite, Welsh doesn't bother with y. Again, like Irish!