On Ubuntu 14.04:

$ nmcli dev list | grep -i dns

On Ubuntu 16.04, first list all the connections:

$ nmcli con show
NAME                UUID                                  TYPE             DEVICE  
docker0             19d065fc-b97f-4421-b839-127d95c07c51  bridge           docker0 

Then list the settings of one connection:

$ nmcli con show docker0 | grep -i dns
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