https://bugs.chromium.org/p/chromium/issues/detail?id=676639
With the above issue fixed, I think this issue is also fixed now since the user only need to click the "Turn on Bluetooth to allow pairing" once and there is no permission prompt shown. So I will mark this issue as WontFix.

What do you think?

Location access still requires us to use an intent and show the system settings activity. That results in the chooser being closed when the user returns. So, this issue is still valid.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/729ec70ac51077fad0c36dc88d8e8a425eb77032

commit 729ec70ac51077fad0c36dc88d8e8a425eb77032
Author: juncai <juncai@chromium.org>
Date: Thu Mar 23 20:18:44 2017

Keep WebBluetooth chooser open when permission prompt is shown on Android

On Android, when WebBluetooth chooser is shown and needs to open
permission prompt, the chooser will be closed. This CL uses similar idea
as:
https://codereview.chromium.org/2622123002/
to keep the chooser open when permission prompt is shown.

BUG= 661862 

Review-Url: https://codereview.chromium.org/2772453003
Cr-Commit-Position: refs/heads/master@{#459197}

[modify] https://crrev.com/729ec70ac51077fad0c36dc88d8e8a425eb77032/chrome/android/java/src/org/chromium/chrome/browser/BluetoothChooserDialog.java
[modify] https://crrev.com/729ec70ac51077fad0c36dc88d8e8a425eb77032/chrome/android/java/src/org/chromium/chrome/browser/ItemChooserDialog.java
[modify] https://crrev.com/729ec70ac51077fad0c36dc88d8e8a425eb77032/chrome/android/javatests/src/org/chromium/chrome/browser/BluetoothChooserDialogTest.java