Move sync_client.cc away from base::Bind

BUG=714018

Change-Id: I59944400286435c71ed605ba019cd7f2680e5532
Reviewed-on: https://chromium-review.googlesource.com/1174656
Reviewed-by: vitaliii <vitaliii@chromium.org>
Commit-Queue: Antonio Gomes <tonikitoo@igalia.com>
Cr-Commit-Position: refs/heads/master@{#584052}
2 files changed