Under the hood, the Bamboo Docker task is using a docker login command line including the meanwhile unsupported --email or -e flag, as confirmed by the resp. issue Docker Task: -e required for docker push command (BAM-18613). The --email or -e flag has been removed as of Docker version 17.06.0-ce, so an upgrade to this or a newer Docker version without an accompanying upgrade of the Bamboo Docker task will yield the exception at hand.
If you cannot upgrade your Bamboo version right away, you might be able to apply one of the following workarounds:
Upgrade only the Bamboo Docker app itself to release 6.2.0, as suggested by Atlassian's Alexey Chystoprudov in his answer to Bamboo Docker Push fails Please note that Alexey emphasizes that they cannot guarantee it is 100% compatible!