Actually update the docs site (#15003)

Fixes https://github.com/flutter/flutter/issues/15002

dev/bots/docs.sh

@@ -35,7 +35,7 @@ cp dev/docs/google2ed1af765c529f57.html dev/docs/doc
 # Upload new API docs when on Travis
 if [ "$TRAVIS_PULL_REQUEST" == "false" ]; then
   echo "This is not a pull request; considering whether to upload docs... (branch=$TRAVIS_BRANCH)"
-  if [ "$TRAVIS_BRANCH" == "master" -o "$TRAVIS_BRANCH" == "dev" ]; then
+  if [ "$TRAVIS_BRANCH" == "master" -o "$TRAVIS_BRANCH" == "beta" ]; then
     cd dev/docs
 
     if [ "$TRAVIS_BRANCH" == "master" ]; then