If you're looking for a Bromite successor, right now best way is to download the uazo builds direct from GitHub: https://github.com/uazo/bromite-buildtools There are some third party tools that will download the releases for you, but I'm fine to just manually pop by the repo whenever ungoogled-chromium[0] updates on my desktop.
So far the uazo builds have only run up to a couple weeks behind Chromium mainline, unlike Bromite which could fall months behind. I'm not sure if there is a better privacy-oriented browser for Android right now if you want just want a stripped back Chromium. The other privacy-oriented browsers all seem to add a bunch of extra stuff.
I need to actually try Fennec one of these days instead letting it sit on my phone.
I still don't exactly trust these builds since they are small fries and I imagine not a ton of people are combing the code to make sure data isnt getting logged somewhere. They are great for browsing the internet, but I typically don't put passwords in them.
Then I learned about Bromium(which is obsolete today, but was a great browser with adblock support)