Currently Initiative (or higher level hierarchy issues) issue color selections don't show up on Kanban boards. The default color is set to Purple for all parent links display on cards. 

It would be great to display the issue color for all issue hierarchies on kanban boards. Issue is described in this community request below:

https://community.atlassian.com/forums/Jira-questions/Colors-can-t-be-changed-for-initiatives-aren-t-represented/qaq-p/2959084#M1112189

Potential Workaround: Card Colors

You might be able to achieve the desired visual effect using Card Colors based on JQL:

1. Go to your board and select Board settings > Layout > Card colours.
2. Change the "Select method" dropdown to Queries.
3. Add a query like issuetype = Program and assign it your preferred color (e.g., Blue).