F-Droid repository
You can download Ungoogled-Chromium-Android through F-Droid client and receive updates through it.
You need to add the official Ungoogled-Chromium-Android F-Droid repository as a third-party repository either by scanning the QR code or adding the URL manually (copy the link from below images). Note that depending on your phone architecture (arm, arm64 or x86), you need to add a different repo:
Arm:

Arm64:

x86:

Always verify that the repository details are exactly:
Arm:
Address: https://www.droidware.info/fdroid/repo
Fingerprint of the signing key: 2144449AB1DD270EC31B6087409B5D0EA39A75A9F290DA62AC1B238A0EAAF851
Arm64:
Address: https://www.droidware.info/arm64/fdroid/repo
Fingerprint of the signing key: 2144449AB1DD270EC31B6087409B5D0EA39A75A9F290DA62AC1B238A0EAAF851
x86:
Address: https://www.droidware.info/x86/fdroid/repo
Fingerprint of the signing key: 2144449AB1DD270EC31B6087409B5D0EA39A75A9F290DA62AC1B238A0EAAF851
Example:

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