Theming views fields with twig
You're probably looking for

views-view-fields--[view-name]--[machine-name].html.twig

views-view-fields--search--results.html.twig

In your view click on your title field and uncheck Link to the content. 

then your template file 

&lt;a href="#" class="search-result__item-title"&gt;{{ fields.title.content }}&lt;/a&gt;


Not really sure if you really want # as href. I think you want to link to content. So add Path as a field.

&lt;a href="{{ fields.path.content }}" class="search-result__item-title"&gt;{{ fields.title.content|striptags }}&lt;/a&gt;


Note: You'll probably want to use |striptags if you do not strip the markup from the views UI. Unless you do not mind having &lt;divs&gt; wrapping your title text. 

then {{ fields.field_machine_name.content }} each of the rest of your fields that you want to output. 


  Important: Make sure TWIG DEBUG is off, as it tends to screw up templates in Views.