There is already a determiner before amis, namely a number (mille un). No article can be used in this case, like in English. (You don't say ten the friends but simply ten friends.)
And if your question is about enfant, the absence of article is due to the fact that it is used as an adjective meaning young.
You'd see this in some pictures titles, such as "Mozart enfant" by Cignaroli
(and for some reason mille et un is more idiomatic than mille un)