Hello @RafaelStein.
You can transfer all your belongings from the Silver server to the Gold server with the Server Transfer feature on the PRO Dashboard. To do so, simply log in, click the "Server Transfer" feature under Tools on the left side, and then click "Transfer for free". It will take a few minutes for the transfer to go through.
You are allowed to transfer for free once every 30 days, however, any subsequent transfers will cost 100 coins. There is currently no cooldown timer for the free transfer, so noting down when you transferred is advisable.
To trade between accounts, you can open two clients and trade with yourself. Do note, that both accounts will need the 4th Kanto badge.
Hopefully this answers your question.