Reland "Remove deprecated flush calls."

This reverts commit 5e6d789ce47c8ce474b597073f7580602fcca467.

Reason for revert: Relanding with fix landed in chrome

Original change's description:
> Revert "Remove deprecated flush calls."
> 
> This reverts commit d8fd0bf5749c62302eb1d1c9f4eaab151d839341.
> 
> Reason for revert: chrome roll
> 
> Original change's description:
> > Remove deprecated flush calls.
> > 
> > Bug: skia:10118
> > Change-Id: I13758b5416784c296b8b5be9f3228230ac1be05f
> > Reviewed-on: https://skia-review.googlesource.com/c/skia/+/290540
> > Commit-Queue: Greg Daniel <egdaniel@google.com>
> > Reviewed-by: Brian Salomon <bsalomon@google.com>
> 
> TBR=egdaniel@google.com,bsalomon@google.com
> 
> Change-Id: I49d35cdb258e632f645974c5ec62075d3392efe0
> No-Presubmit: true
> No-Tree-Checks: true
> No-Try: true
> Bug: skia:10118
> Reviewed-on: https://skia-review.googlesource.com/c/skia/+/290834
> Reviewed-by: Greg Daniel <egdaniel@google.com>
> Commit-Queue: Greg Daniel <egdaniel@google.com>

TBR=egdaniel@google.com,bsalomon@google.com

# Not skipping CQ checks because this is a reland.

Bug: skia:10118
Change-Id: Ie24d7845a4ad75f95afe59037ea80a9f38082f13
Reviewed-on: https://skia-review.googlesource.com/c/skia/+/290918
Reviewed-by: Greg Daniel <egdaniel@google.com>
Commit-Queue: Greg Daniel <egdaniel@google.com>
10 files changed