In the bamboo UI, builds that have child builds have a list of those builds under the tab marked "dependencies". This list was accessible from an API call at least as of version 5.5, possibly later:
https://docs.atlassian.com/bamboo/REST/5.5.0/#d2e3
However, the call responded with a list of all builds. There were other forum questions about this, that have as far as I can tell have been deleted, and the documentation was changed to say "available child dependencies"
https://docs.atlassian.com/bamboo/REST/5.13.2/#d2e28
Right now to get a list of child builds I am scraping the page. Just saying, you're getting that list from somewhere (class DependencyChainListener?) so exposing that list to the API in some fashion would be a big help.
Even I am looking for API to give me list of associated child builds. +1 vote