You should not be directed to the Adobe Store for purchase since you are a paid subscriber to the Creative Cloud.
Not quite sure what you mean by my Creative Cloud Dashboard, but am assuming you mean the Creative Cloud Apps page at https://creative.adobe.com/apps.
From the Creative Cloud Apps page you can click on the Learn More link for Story Plus. The experience is different depending on whether or not you are signed in or with your Adobe ID:
- If you are not signed in then Learn More takes you to the Adobe Story Product Page at http://www.adobe.com/go/storyinfo.
- If you are signed in then Learn More takes you to the Adobe Story Landing Page at https://story.adobe.com/.
From the Adobe Story Landing Page at https://story.adobe.com you can sign in Sign In, Join or Subscribe. If you are a Creative Cloud paid subscriber then you can just Sign In.
Clicking Sign In should bring up an overlay dialog that accepts your Adobe ID and signs you into the application.
Let me know where your experience is different and perhaps post screenshots.