What is equivalent to animation painter in Libreoffice Impress

Short of hacking the .odp file itself, as described in this related 2016 LibreOffice Forum thread and repeated here, there is currently no way to do what you're asking.

1. Open the file with some kind of archive management program.
2. Extract contents.xml.
3. Open in in a file editor. It better be one which can format XML files, since all text in the file is on the same line.
4. Find the relevant anim:par element.
5. Set smil:begin="1s" on the relevant elements.
6. Save the file.
7. Put the file back into the .odp file.

That said, I can confirm that the hack does work, as I've used it myself in the past for instances similar to your own.

LibreOffice Impress has no equivalent tool for the animation painter in PowerPoint yet, to this answered date. Such feature has been requested for some time without any progress.

Known methods fail

The following copy actions in LibreOffice Impress have been tested and failed to duplicate objects with custom animation.

• Copy and paste (Ctrl+C, Ctrl+V): Creates a copy of object without custom animation.
• Ctrl+ drag (with Copy when moving option active): Same as "Copy and paste".
• Clone Formatting Tool (the paint brush icon on toolbar): Copies only the object formatting.

None of these was able to do similar to duplicate animations with the animation painter. In fact, the custom animation is not part of the object formatting.

Why does not work

There is one way of copying existing object with custom animation that actually works within LibreOffice Impress: Create objects with custom animation in a slide, then duplicate the slide.

The duplicate objects however, will lose their custom animation when cut and paste back to the original slide. This suggests that the copy action will only work for objects on different slides and the animation settings per object cannot be duplicated.

In short, duplicate objects with custom animation works at slide-level but not at object-level.

Will ever be implemented

There is a bug report that was filed in late 2011, but not implemented yet.

Bug 43045 - Impress functionality request: add a one click (one key) command to apply a Custom Animation command to selected objects w/o using tasks menus

• Reported: 2011-11-17 12:51 UTC by ade
• Modified: 2018-10-13 18:42 UTC [...]

Another bug report was filed in early 2015, but similarly not implemented yet.

Bug 88938 - SIDEBAR: Copy and paste custom animation style

• Reported: 2015-01-30 12:45 UTC by Yousuf Philips (jay) (retired)
• Modified: 2017-08-31 12:34 UTC [...]

The latter recently gained attention in August 2017, which suggests someone at least understand or aware of the missing feature. We are yet to see such feature to be made available in LibreOffice.