For cheaper kids clothes, try the side streets of the Chunxi Lu shopping area, there are two or three corridors on ground floor and at least one below ground floor full of kids clothes shops. Similar shops can also be found in the clothing area of Lotus wholesale market (HeHuaChi).
For more expensive things, also in Chunxi Lu the large malls such as Chicony, Isetan, each have a whole floor full of kids things (clothes, shoes, toys, etc.). Just as the MixC mall, Global Center and other large malls.
And then of course there is the H&M for good quality foreign stuff, but it is more expensive than in Europe. H&M is all over Chengdu, but there is also a branch in Chunxi lu. And Uniqlo has good basics.