Your address is your unique identity on the Sui network, starting with 0x. Depending on the environment from which you use your Slush app, you should be able to find your Slush wallet address by navigating from the Home Screen to your account, either by selecting the account via the top-right icon or by selecting Profile from the bottom aisle. Then, from the Current Account menu or from the Manage Account menu, you can copy your wallet address.
If you are using the Slush app on mobile, you can use the QR code icon next to Your Coins on the Home Screen to have a QR code generated for your wallet address or to copy the address from the Receive SUI submenu.