acf.php

<?php

function acf_json_save_point ($path) {
    return __DIR__.'/data/acf';
}

function acf_json_load_point ($path) {
    return [__DIR__.'/data/acf'];
}

function acf_load_template_field_choices($field)
{
    $field['choices'] = [];

    $include_paths = [
        get_template_directory() . '/templates',
    ];

    $templates = [];

    foreach ($include_paths as $include_path) {
        foreach (glob($include_path . '/*.php') as $template) {
            if (!in_array($template, $templates)) {
                $templates[] = [
                    'path' => $template,
                    // We get the name of the template by reading the File Header.
                    'name' => get_file_data($template, ['name' => 'Template Name'])['name'],
                ];
            }
        }
    }

    foreach ($templates as $template) {
        $path = pathinfo($template['path'])['filename'];
        $name = $template['name'];

         $field['choices'][$path] = $name;
    }

    return $field;
}

add_filter('acf/settings/save_json', 'acf_json_save_point');
add_filter('acf/settings/load_json', 'acf_json_load_point');
add_filter('acf/load_field/name=template', 'acf_load_template_field_choices');

functions.php

<?php
/**
 * ACF Partials
 *
 * When you define a new content block in ACF, you'll need to create a partial file called partial-*.php
 * within your theme's partials/ folder. The * being the slug of the content block. It must be exactly the same,
 * otherwise it will not load.
 *
 * @param null $post_id
 */
function templatePartials($post_id = null)
{
    // Create an array to hold the content blocks. This keeps them in order.
    $results = [];

    // Can optionally pass a post ID. If not set, get the one within the loop.
    if (!$post_id) {
        $post_id = get_the_ID();
    }

    // Check to see if this post has any Flexible Content layouts set.
    // The Flexible Content field should be named 'layout'
    if (have_rows('layout', $post_id)) {
        while (have_rows('layout', $post_id)) {
            the_row();

            // I usually create a Layout called Template Picker with a Select field called 'Template'.
            // I populate this select field with files that are located inside my theme's templates/ folder.
            // Sometimes we'll build templates that don't need to be configured at all, like a recent posts carousel.
            // This is totally optional, but lets you know you can do different things with different layouts.
            if (get_row_layout() === 'template_picker') {
                $file_name = basename(get_sub_field('template'), '.php');
                $template = substr($file_name, strpos($file_name, '-') + 1);

                ob_start();
                get_template_part('templates/template', $template);
                $results[] = ob_get_clean();
            } else {
                ob_start();
                get_template_part('partials/partial', get_row_layout());
                $results[] = ob_get_clean();
            }
        }
    }

    foreach ($results as $result) {
        echo $result;
    }
}

theme directory structure.txt

themes/
|── my-theme/
│   ├── includes/
│   |   ├── data/
│   |   |   └── acf/ [bunch of .json files in here]
│   |   └── acf.php
│   ├── partials/
│   |   ├── partial-example.php
│   |   └── partial-another-example.php
│   ├── templates/
│   |   ├── template-example.php
│   |   └── template-another-example.php
│   └── functions.php