You can set up a search from to search within the Directory Listings only, or filter the results based on the Custom Fields you’ve set up.

1) Add a new search form via Search & Filter > Add New Search Form

2) In the General tab set Search in the following post types to Directory

Nettl :Directory - Search Form General Settings

3) In the Display Results tab set Display results method to Post Type Archive
And Ajax to the setting in the below screenshot:

Nettl :Directory - Search Form Display Results

4) Drag and drop search form fields form the Available Fields box into the Search Form UI, as required.
For Post Meta fields, make sure that Is ACF Field is checked.
An example of adding a dropdown box to filter Listings by Directory Categories.

Nettl :Directory - Search Form Taxonomy Filter Example

An example of adding a filter by Custom Field option:

Nettl :Directory - Search Form Post Meta Example

How the example form display on the front end of the website:

Nettl :Directory - Search Form Front End