How do I use dpm() or kint() to debug a block plugin I created?
dpm() definitely works within a custom block; I just tested. Since it calls a service, you may need to clear your cache before it shows up, for example with the command line with drupal cache:rebuild all or drush cr.

To test if the service is available, you could use this code.

dump( \Drupal::service('devel.dumper')); die();


Another thing to consider is that blocks are cached in Drupal 8 by default.  Make sure your build() is actually executing. You may want to turn off the rendering cache while developing, in settings.php or settings.local.php.

$settings['cache']['bins']['render'] = 'cache.backend.null';