how to save image custom attribute in magento 2

In your observer there is a lot of unnecessary code. You can change it like:

<?php

namespace Dcw\Vm\Observer;

use Magento\Framework\Event\ObserverInterface;

class ProductSaveAfter implements ObserverInterface {

    protected $request;
    protected $resource;

    /**
     *
     * @param \Magento\Framework\App\RequestInterface $request
     * @param \Magento\Framework\App\ResourceConnection $resource\
     */
    public function __construct(
        \Magento\Framework\App\RequestInterface $request, \Magento\Framework\App\ResourceConnection $resource
    ) {
        $this->request = $request;
        $this->resource = $resource;
    }

    public function execute(\Magento\Framework\Event\Observer $observer)
    {
        $data = $this->request->getPostValue();

        if (isset($data['product']['media_gallery']['images'])) {
            // print_r($images);exit;
            $connection = $this->resource->getConnection();
            $tableName = 'catalog_product_entity_media_gallery'; //gives table name with prefix
            $product = $observer->getProduct();
            $mediaGallery = $product->getMediaGallery();

            if (isset($mediaGallery['images'])) {
                foreach ($mediaGallery['images'] as $image) {
                        //Update Data into table
                    $vmValue = !empty($image['vm']) ? (int)$image['vm'] : 0;
                        $sql = "UPDATE " . $tableName . " SET vm = " . $vmValue . " WHERE value_id = " . $image['value_id'];
                        $connection->query($sql);
                }
            }
        }
    }

}

Because you don't need to store data from a request, as it has no value_id in newly created images, therefore your data didn't remain when adding the new image.

To get data in other places I wrote a plugin. It's adding the column vm to media gallery select:

app/code/Dcw/Vm/etc/di.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
    <type name="Magento\Catalog\Model\ResourceModel\Product\Gallery">
        <plugin name="afterCreateBatchBaseSelect" type="Dcw\Vm\Plugin\Product\Gallery" sortOrder="10" disabled="false"/>
    </type>
</config>

Code:

<?php

namespace Dcw\Vm\Plugin\Product;

class Gallery
{
    public function afterCreateBatchBaseSelect(
        \Magento\Catalog\Model\ResourceModel\Product\Gallery $subject,
        \Magento\Framework\DB\Select $select
    ) {
        $select->columns('vm');

        return $select;
    }
}

So now your custom attribute vm should always exists in the products media data.

To hide the vm-images on the frontend you can write plugin:

app/code/Dcw/Vm/etc/frontend/di.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
    <type name="Magento\Catalog\Model\Product">
        <plugin name="afterGetMediaGalleryImages" type="Dcw\Vm\Plugin\Product" sortOrder="10" disabled="false"/>
    </type>
</config>

Code:

<?php

namespace Dcw\Vm\Plugin;

class Product
{
    /**
     * @param \Magento\Catalog\Model\Product $subject
     * @param \Magento\Framework\Data\Collection $result
     * @return mixed
     */
    public function afterGetMediaGalleryImages(\Magento\Catalog\Model\Product $subject, $result)
    {
        foreach ($result as $key => $image) {
            if ($image['vm']) {
                $result->removeItemByKey($key);
            }
        }

        return $result;
    }
}

To obtain the vm-images from the product, use code writen by @Marius (without a plugin that deletes this images):

$images = []; 
foreach ($product->getMediaGalleryImages() as $image) {
    if ($image->getVm()) {
        $images[] = $image;
    }
}

Retrieving in frontend:

Let's say that the product for which you want to display the virtual mirror is $product.
You can get the images that are marked with your custom attribute like this:

$images = []; 
foreach ($product->getMediaGalleryImages() as $image) {
    if ($image->getVm()) {
        $images[] = $image;
    }
}

Then you can loop through the $images array and display them where you need.

To save the value of that checkbox in the backend I think you need to write an after plugin for the method \Magento\Catalog\Model\Product\Attribute\Backend\Media\ImageEntryConverter::convertFrom where you attach the value you get from post in the $entryArray.