Is there are any way to track how many visitors come from a social media channel like Facebook to a landing page and from here to an external page (although an affiliate)?
You can certainly do this! You may need to edit links and add tracking so that GA can distinguish the traffic you're interested in, but nothing technically complicated.
First, to track inbound traffic from your own social media pages specifically, you'll need to tag your links with UTM parameters. I would suggest keeping the source as the social media channel, setting medium to something neutral like "social", and using campaign to identify these links. Something like:
Edit the links you post on social media to include those parameters, and visits from people clicking on them will show in GA as having a Campaign of "owned-social", which you can filter and segment on. "Owned social" is quite generic for a campaign name, and you can make it more specific to what you are trying to do; it just needs to be unique.
Google has a Campaign URL Builder that will speed up the process of making versions of these links for different channels, and help avoid typos.
Tracking of landing pages is automatic; nothing needed there.
For the external link, you must track clicks on the appropriate links as an Event in GA. You could have a Category of "Outbound Link", Action that denotes the affiliate linked to (I will use "Affiliate" as a placeholder), and optionally a Label with additional detail, such as which link the person clicked if there is more than one on the page.
Once you have that all in place, you can use a segment to track how many people went from point A to B to C. You'll defined a session-level segment with 3 filters.
In the Traffic Sources panel of the segment builder, set
exactly matches owned-social. In the Conditions panel, set
Landing Page to
starts with /landing-page, and
Event Action to
exactly matches Affiliate. (These last should be joined by
and, which will happen automatically if you use the "Add Filter" button, or can be selected when adding a condition to the first filter.)
You won't even have to save your segment to see the totals and percentage of traffic meeting these criteria - it will appear in the right-hand column of the segment builder. And if you check those numbers before adding the Event filter, you'll be able to calculate what percentage of the people who arrived at your landing page from your social media clicked through on the affiliate link.
[By "people" I mean "sessions", really, but proportionally you should get a good sense for how enticed people are to click through.]