I have seen few apps which are able to embed links in the response of Standard card in Alexa. for eg :: see the skill : https://www.amazon.co.uk/Guardian-News-Media-The-US/dp/B01N5HQRUC
They are able to show the links in the standard card response. Something like this
The documentation of the Alexa skills does not say anything about urls in the card response.
Looks like it is a special skill called Flash Briefing skill. Though feed skill is still rendering as standard card, Amazon has not made embedding a link in the card response in custom skill available to public.
check the documentation: alexa documentation
See this link. In the table there is something called display Url which will be rendered as the read more link in the card.