[flutter_plugin_tools] Move license-check tests to runCapturingPrint

[stuartmorgan]

Eliminates the custom printer in the command, and updates the tests to use the repo-standard runCapturingPrint.

This avoids unnecessary divergence of test styles, and simplifies the command itself. It was only written the other way in the first place because I wasn't aware of runCapturingPrint.

Pre-launch Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the Tree Hygiene wiki page, which explains my responsibilities.
• I read and followed the relevant style guides and ran the auto-formatter. (Note that unlike the flutter/flutter repo, the flutter/plugins repo does use dart format.)
• I signed the CLA.
• The title of the PR starts with the name of the plugin surrounded by square brackets, e.g. [shared_preferences]
• I listed at least one issue that this PR fixes in the description above.
• I updated pubspec.yaml with an appropriate new version according to the pub versioning philosophy.
• I updated CHANGELOG.md to add a description of the change.
• I updated/added relevant documentation (doc comments with ///).
• I added new tests to check the change I am making or feature I am adding, or Hixie said the PR is test exempt.
• All existing and new tests are passing.

[gaaclarke]

lgtm