@Vaughn Shideler
I don't see why you are logged in as root , usually ambari-qa or Admin
I see you should have set it a directory higher, the offending directory permission is on SourceCluster
# hdfs dfs -ls -d /apps/falcon/SourceCluster/staging
drwxrwxrwx - root hdfs 0 2018-05-10 03:41 /apps/falcon/SourceCluster/staging
So as hdfs user run the below snippet
$ hdfs dfs -chown -R falcon /apps/falcon
Then proceed as below
I have just tried out on my Single node cluster HDP-2.6.2.0 falcon 0.10.0
The Falcon UI will accept Admin, hive or Falcon and NOT prompt for the password so you can log out and log in as admin or falcon.
It's important the user has a home under /apps/* so in your case, you can use falcon form the above sequence. Below is the my output.
$ hdfs dfs -ls /apps
Found 4 items
drwxrwxrwx - falcon hdfs 0 2018-05-04 17:48 /apps/falcon
drwxr-xr-x - hdfs hdfs 0 2017-10-19 13:43 /apps/hbase
drwxr-xr-x - hdfs hdfs 0 2017-10-19 13:53 /apps/hive
drwxr-xr-x - zeppelin hdfs 0 2017-10-19 19:25 /apps/zeppelin
See attached screenshot.
Please revert