Download the .dmg from /download. Open it, drag UniFlow Trans.app into your /Applications folder, and open it from Spotlight.
On first launch, macOS will ask for microphone permission. Grant it — the app can't record otherwise. You can later revoke it in System Settings → Privacy & Security → Microphone.
You'll see a one-time onboarding flow that asks you to sign in with the account you created at uniflowtrans.com, then prompts you to pick a source and target language. That's it.