For the life of me, I can’t seem to figure that out. I have them working locally and through the my.openhab dashboard, just not on the app.
This seems to be a little mystical, some got it going, others not. Aren’t they displayed at all or is it only the dynamic part which isn’t working?
For me it’s working and here are some tipps (all are related to OH2 installations. I have also used custom icons in my old OH1 days, but I couldn’t remember what I’ve done there to get them going… 
):
Some people have said that the ios app only supports png icons (not svg). I haven’t checked this but I am using png and they do work.
You have to define png as default both for the Basic UI and the Classic UI. You can do that in the appropriate file or in PaperUI settings for the both UI bindings (I would suggest PaperUI). Otherwise svg would be the standard.
The custom icons have to be stored in conf/icons/classic/ (doesn’t matter if you use BasicUI or ClassicUI, both take them from this folder).
And sometimes it helps to use “clear cache” in the iOS app, or even reboot your OH installation.
For the use of dynamic icons, this is another story to be told… 
It ended up working all of the sudden. But I’m not sure what fixed it. I have both the .svg and .png version of the icons in the conf\icons\classic folder. I restarted OH2 and cleared the cache. Waited for a while. Posted this topic. Waited some more. Went home… Checked my iPad and it had the icon! Check my iPhone it finally had it! I’m wondering if it needed to be on my home network??
So dynamic custom icons work, we just don’t know how. I would say .png files in the classic folder following the dynamic icon rules (basefile.png, basefile-state1.png, basefile-state2.png,…), and some patience OR home network.
And BTW, I have OH2 UIs configured to use vector (.svg).