After looking at an article on InsightScope about contest giveaways, I just read the FAQs for one of the tools, which is KingSumo Giveaway and I see that as at the time the FAQs were prepared, the tool doesn't integrate with Mailchimp. Instead you have to download a CSV and upload.
Also, there is a warning that the tool may not be compatible with Facebook's terms in the future.
Finally, there is a long, convoluted way you have to deal with duplicate content, which is described in the FAQs as follows:
I’m concerned about duplicate pages for SEO We don’t create new pages, just add a parameter to your URLS. Google just sees the original page and URL structure. What we recommend if Google results are important is to run the tool, then once it looks like a winner I’d change the Title to the winner and the original URL. Remove the other titles. We are working on a fix to make this easier.
Utilize the parameter tools in Google’s Webmaster Tools and set the Headline plugin’s unique parameter as “Representative URL.” You’ll find this in Webmaster Tools under “Crawl > URL Parameters.” More details on the setting URL parameters can be found at this Google support document. Make sure you have canonical URLs setup on your WordPress website. Many SEO plugin tools will have this available out of the box, with the popular tool being Yoast’s WordPress SEO Plugin. More details on canonical URLs usage scenarios can be found at the Google documentation here.
So I asked KingSumo:
1. Does Giveaways integrate with Mailchimp marketing service?
2. Is Giveaways compliant with Facebook’s terms of service as of now, March 2015?
3. Any updates on a fix to make dealing with duplicate pages for SEO easier?
I'll update this when I hear back.