Tell SuperSide Me (2.4.0) to use your theme's SVG icons.

supersideme-svg_01.php

<?php

add_filter( 'supersideme_svg', 'leaven_prefer_theme_svg' );
/**
 * Tell SuperSide Me not to load any icons.
 * @param $args
 *
 * @return mixed
 */
function leaven_prefer_theme_svg( $args ) {
	$args['styles'] = false;

	return $args;
}

supersideme-svg_02.php

<?php

add_filter( 'supersideme_svg', 'leaven_prefer_theme_svg' );
/**
 * Let's load completely custom icons which aren't somehow otherwise being loaded.
 * @param $args
 *
 * @return mixed
 */
function leaven_prefer_theme_svg( $args ) {
	$args['styles'] = array( 'custom' );
	$args['path']   = get_stylesheet_directory() . '/sprites';

	return $args;
}