(for archeology purposes, can you briefly describe the motivation for this change? thanks)

This LGTM, would also appreciate the explanation. It looks to me like this was added as a way to set the local engine before we could just pass --local-engine to the command, and now that we can do that it gets confusing when both are set.

The devicelab script contained a feature that was intended to let you run a devicelab test with a local engine build by setting the FLUTTER_ENGINE environment variable. I don't know if this feature was ever widely used. But it was placing the --local-engine flag in the wrong place in the flutter_tools command line, so it doesn't currently work.

Recently a --local-engine flag was added to the devicelab command line. That flag works for most devicelab tests (which run flutter_tools through functions in lib/framework/utils.dart). This PR updates the remaining tests to support the --local-engine flag and removes the obsolete FLUTTER_ENGINE variable.