You can find free knitted poncho patterns for kids from online knitting pattern directories and online or physical yarn-selling shops. Pinterest is also a good resource for free knitting pattern searches.
Knitting pattern directories, such as AllFreeKnitting and Knitting Pattern Central, offer a number of free patterns under different categories. Look under children knits, baby knits, ponchos and sweaters to find poncho patterns for kids. You can also use Pinterest to look for free patterns. Put "free patterns for kid ponchos", for example, into the search bar, then choose the photos that you like and follow the links attached.
Online shops, such as Knit Picks, Red Heart, and Craftsy, give away a collection of free patterns besides their paid patterns and yarn. You can use the search bar on Craftsy's Knitting Blog to look for poncho patterns for kids. Knit Picks and Red Heart have customized pattern searches which allow filtering patterns by knitting or crocheting, free or paid, the level of difficulty for the thing you want to make.
Some local yarn shops occasionally give away free patterns. Visit your local shops and talk to the shopkeepers for more information.