To update the embedding dependencies, just cd into this directory, modify the dependencies in build.gradle and run gradle updateDependencies.
Once you have updated the dependencies, you can upload a new version by running cipd create --pkg-def cipd.yaml. For more, see the Chromium instructions on “Updating a CIPD dependency” for how to upload a package update to CIPD.
On successful upload, you will receive a hash for the upload such as
cipd: successfully uploaded and verified flutter/android/embedding_bundle:NZvE-rL3E66nHQZb5Vyl9-1Y_1MWEX7KURgOHqX2cYcC
Let's further annotate the new upload with the current timestamp.
$ cipd set-tag flutter/android/embedding_bundle --version=<new_version_hash> -tag=last_updated:<timestamp>
Example of a last-updated timestamp: 2019-07-29T15:27:42-0700
You can generate the same date format with date +%Y-%m-%dT%T%z.
You can run cipd describe flutter/android/embedding_bundle --version=<new_version_hash> to verify. You should see:
Package: flutter/android/embedding_bundle Instance ID: <new_version_hash> ... Tags: last_updated:<timestamp>
Then update the DEPS file (located at /src/flutter/DEPS) to use the new version by pointing to your new last_updated_at tag.
  'src/third_party/android_embedding_dependencies': {
     'packages': [
       {
        'package': 'flutter/android/embedding_bundle',
        'version': 'last_updated:<timestamp>'
       }
     ],
     'condition': 'download_android_deps',
     'dep_type': 'cipd',
   },
You can now re-run gclient sync to fetch the latest package version.