
You can use a name if there is no likelihood of confusion with an existing trademark. US law is based on use and not merely registration. So even if it looks clear on the federal trademark register, you still need to search for potential "common law" use of a confusingly similar brand.
Flying and Flying X for the same goods will likely be confusingly similar.
It is all about protecting the consumer. If a consumer saw the Flying brand on clothing, would they think that similar clothing with the Flying X brand on them were from the same or a related source?