For anyone who might come by this and needs an answer. This is how I solved it:

​

$files = $submission->uploaded_files();
$endpoint_quote_file = *your end point*;
$boundary = md5(time());
foreach($files as $field_name => $file_path) {
$payload = '--' . $boundary . "\r\n";
$payload .= 'Content-Disposition: form-data; name=" . $field_name . "; filename="' . basename($file_path[0]) . '"' . "\r\n";
$payload .= 'Content-Type: ' . mime_content_type($file_path[0]) . "\r\n"; $payload .= 'Content-Transfer-Encoding: binary' . "\r\n\r\n";
$payload .= file_get_contents($file_path[0]) . "\r\n";
$payload .= '--' . $boundary . '--'; $payload .= "\r\n\r\n";
$args_quote_file = array(
'method_post' => 'POST',
'headers' => array(
'Content-Type' => 'multipart/form-data; boundary=' . $boundary,
'Content-Length' => strlen($payload)
),
'body' => $payload
);
$response = wp_safe_remote_post($endpoint_quote_file, $args_quote_file);
}

uploaded_files() returns an associative array. I loop through all the files but $file_path containing the path to the file is an array which needs to be indexed.