Make sure that you tell your router to use your PI3 for DNS Services (Change DNS Settings).
Bear in mind that most routers have two DNS addresses in their settings, in my case my router would use either DNS address, this meant that sometimes my *.duckdns.org address did not resolve. To fix this I installed DNSMasq on a second (always on) device on my network. ie the router points to two identically configured DNSMasq servers on my network.
The other option is to leave the second DNS setting blank (NOT RECOMMENDED); but if you do this there will be no redundancy in your system and if your DNSMasq server goes down this will cripple your internet access.