I can imagine that this is supposed to work as follows: You run an update client to keep your DynDNS hostname updated with your IP address information, and that Proxy DNS service provider frequently looks up your DynDNS hostname to obtain your IP address, given that you entered your hostname at their website.

In case your service provider is www.smartdnsproxy.com - this is what they say at their website:

you can use Dynamic DNS services such as DynDNS or NoIp to automatically update your IP. Please obtain a dynamic DNS host address from one of the dynamic DNS service providers of your choice, and then enter your host address under profile section in your account. We will use this host address to automatically update your IP every time it changes, this means no more interruptions in your service when your ISP decides to change your IP.

Regarding your IP address information updates, you can use one of many DDNS update clients, like a software on a computer (such as Dyn's client) or a built-in DDNS service on your router, NAS, DVR, IP camera, etc.  But use only one update client at any time for a specific hostname.

If you use your DynDNS hostname only to keep this Proxy DNS provider updated, and you use this PC where you run the Dyn Updater to access Netflix etc, then this configuration should be sufficient for your purpose, because the IP address information does not need to be current outside of the usage.  If you decide to use your router's built-in update client, then you configure it like this:

Service Name: probably selectable from a drop-down list, something like Dyn.com, dyndns.org or such 

Domain Name; your full DynDNS hostname, like example.dyndns.org

User Name: Your Dyn username (not the e-mail address!)

Password: your Dyn account password or your Updater Client Key

This should keep your hostname updated with your IP address information in case your router is working properly.