Bug 1253740 added an implementation of chrome.storage.sync, but this implementation doesn't actually sync on Android due to the difference of what parts of Sync that ship on Android. This means that although chrome.storage.sync works on Android, it doesn't sync.
Per discussion, we will consider this bug in the scope of WebExtension; and already added this bug into the metabug list of Bug 1185785 - (webext-android) [tracking] Extension API for Android. We are removing the tracking-fennec flag for now, please feel free to re-nominate if needed. Thank you very much !