How can I show an image in a view using the Search API Views integration?
You're on the right track. To achieve this in Views:


Add the indexed image field to the View Fields list
Set 'Display' to 'Show entity label' 
Untick 'Link to entity' - this adds additional HTML in the token used below that will stuff things up
Select 'Rewrite output of this field', and use this code:

&lt;img src="/sites/default/files/[field_files_file]" /&gt;


Check the token is right, under 'Replacement tokens', but this should allow you to render the image into the View output. 

From here, you can specify any inline attributes you want, e.g. width, height and so on. 

You could achieve a thumbnail look this way, or alternately you could use image styles to generate a thumbnail of the image your users upload, then index that field instead. Note that image styles will save your new image under a different directory, so sites/default/files won't work.