Does the Doctrine of No Soul mean there is nothing permanent to continue?
I agree with you.

The Pali suttas do not refer to a continuous consciousness at the termination of life. 

Instead, the suttas explain 'birth' ('jati') &amp; 'death' ('marana') refer to the birth &amp; death of 'self-views'.

Therefore, 're-birth' refers to the re-arisings of 'self-view'. 

For example, you make $100,000. Re-birth is the happy view: "I made $100,000; I am rich". You lose $100. Death is the unhappiness of 'I lost $100; I am poor".