How do I retrieve my Game Center username and password from my iPhone to my Android, so I can restore the progress of my Clash of Clans app?
You don't need your Game Center user and password —which in any case is usually your Apple ID and password; you can link devices in-game.
From the Supercell support site, specifically "Transferring your game to another device":
iOS > Android or Vice Versa
First, make sure the game is installed on both devices, keeping them both on-hand. Use the “Link a device” feature in the in-game settings, and then select “Link a device” on both. Follow the on-screen instructions to complete the transfer.
The username and password are not stored in plain text.
I would open a support case with the vendor and link to the article they send you if you need help implementing a specific step in the process (since you might not even need to know the password to resume your clan).
Here's what you can do on the iPhone