How? Like Hubitat's Hue Bridge integration, it's just another app written on top of Hue's excellent, local, well documented API. There is nothing either app could do that the other can't (and certainly not a question of how given that it's documented), just a question of who chose to implement was to do what parts of different things in that API.
If you want to initiate a Hue feature that Hubitat doesn't support (e.g., start the "colorloop" effect on one of your Hue bulbs)--which as far as I remember the Hue app itself doesn't either--you could use this app to do that manually, I guess.
Oh, I was wondering if this could integrate colorloop and that flash effect we talked about before
The Hue API does not provide a native "flash" capability, presumably because the bulbs themselves don't. Anything there would be emulating that (which would probably be pretty reliable with Hue). The Hue API does provide a "colorloop" effect. I assume this app might provide access to that (I haven't looked at the code to know for sure), but it wouldn't really help Hubitat--it's a desktop app that Hubitat has no way of accessing, and there's no need: both this app and Hubitat's integration app are just using what the Hue API exposes. Hubitat happens to have just not implemented a way to start/stop the "colorloop" effect, possibly because it doesn't align with any standard Hubitat capbility in their device model.
Breathe on repeat would “flash”
Who can I tag to ask if they’d look into adding “breathe”
It's not really a blink--it slowly fades the brightness up and down (I guess the analogy would be breathing). It's meant for identifying bulbs, e.g., when you add a bunch to the Hue app and want to know which is which, a tap on the bulb in the app will run one cycle. Hubitat has barely touched the Hue integration since it was added--I only remember there being one fix for multiple Bridges set up in the integration app--so I wouldn't count on this getting added natively any time soon.
Wouldn’t hurt to ask? Who would I ASK?
I'm guessing @mike.maxwell wrote the Hue Bridge integration , so maybe him, but I'd also guess he's too busy working through the wishlist of new Zigbee devices to touch an integration that works fine enough already. I think your best bet is waiting for a community integration that might include this feature. (Or if you're familiar with the Hue API, you could use Hubitat to send ant HTTP PUT with the appropriate parameters to the Bridge yourself, but that's a lot of work if you aren't.)