Create form which redirects to site in network?

You could perform a validation through get_blog_id_from_url($domain, $path) function, assuming you are using directories and NOT subdomains. Otherwise, $path is not required.
See code and comments below.

<?php
if ( ! empty( $_POST['sitename'] ) ) {
    $main_site_url = network_site_url( "https://wordpress.stackexchange.com/" );
    $domain        = preg_replace( "/^https?:\/\/(www)?/", '', $main_site_url );

    $path = preg_replace( "/\//", '', trim( $_POST['sitename'] ) );
    $path = preg_replace( "/^(.+)$/", "/$1/", $path );

    // If the sitename does not exist.
    if ( ! $blog_id = get_blog_id_from_url( $domain, $path ) ) {
        // Perform whatever you want here...
        wp_die( 'Sitename does not exist.' );
    } else {
        wp_redirect( get_site_url( $blog_id ), 302 );

        exit;
    }
} ?>
<form name="linkform"
      id="linkform"
      method="post"
      action="">
    <p>
        <label for="sitename">Site Name:</label>
        <br><input type="text" name="sitename" id="sitename" value="" size="50"/>
    </p>
    <p class="submit">
        <input id="submit" type="submit" name="Submit" class="submit" value="Go"/>
    </p>
</form>

Put the PHP code plus the form HTML in the same place/page.

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