For most airlines there is not a dress code for first class.
However when flying first class business casual clothing is appropriate although you can also wear cargo pants, comfortable shoes and a long sleeved shirt or T Shirt.
Even if an airline does not have any dress code for the business class or first class flight you should also consider the purpose of your first class or business class trip on the plane and dress accordingly.
Other good clothing options for first class flights are slacks, skirts, or even chinos and you can pair these along with blouses or shirts for a more formal look in first class.
Chinos or trousers and a shirt are a good option for men to wear in first class.
And tight black trousers or even a blazer or dress is good for women in first class.
When flying first class you should avoid wearing clothing which exposes your torso and avoid clothing with any offensive languages.
You should also avoid wearing Athletic wear or Pajamas in first class or business class.
When choosing the proper clothing for first class or business class flights you should also considered the length of your flight, purpose of the flight and comfort.
Some airlines however do provide pajamas for long haul flights.
And some airlines also prohibit being in your bare feet and airlines can also remove any passengers who have attire, odor or bad hygiene that creates and offense or unreasonable risk to other passengers.