Getting all child issues of an initiative via JQL is possible since Portfolio 2.10, you can check the details here: https://confluence.atlassian.com/jiraportfolio/portfolio-for-jira-2-10-release-notes-940678731.html#PortfolioforJira2.10releasenotes-childissues
At the moment it does not appear to be possible. Initiatives are a function of JIRA portfolio, and at least at this time, this relationship is not searchable via JQL, even with 3rd party add-ons.
I would refer you to this other related community post: https://community.atlassian.com/t5/Answers-Developer-Questions/JIRA-Portfolio-How-do-you-configure-the-issue-link-type-is-used/qaq-p/549892
There is an existing feature request to have the parent link behave in the same way as epic link does (which in turn would allow for the JQL searching of this kind)
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG
We're bringing product updates and pro tips on teamwork to ten cities around the world.Save your spot