You can install the iOS app or the Android app to use Google Inbox on a mobile device. For now, Google Inbox doesn't support mobile browsers.
Inbox no longer requires Chrome for desktop. In addition to Chrome, Inbox now supports Firefox and Safari. For some reason, Internet Explorer is still not supported. Here's the error message displayed by Inbox: "Oops, your browser is not yet supported. Inbox works best on Chrome, Firefox, or Safari. More browsers coming soon."
There's also an error message for old versions of supported browsers: "It's been a while since your browser was last updated. Please upgrade to the latest version to continue using Inbox."
"If you aren't using Inbox yet, now's a perfect time to jump in. Email email@example.com to request an invite and we'll email you as soon as more invites are available," informs Google.