There are a few ways you can do this. Retrieving a Blog RSS feed is quite simple, and there are a number of libraries, such as jFeed that might work.
In short, this would call the RSS feed (assuming its public) and then make it available to the external HTML page. If the site is secured, then you'll either need to grant access and/or create a user to allow the RSS feed to be seen. Using a simple HTTP Basic Curl request with basic caching (with a simple cron), is a very easy and common pattern I have seen.
Hope that helps. =)