How can I sign in to Vinted on my Android phone,

Start with this: Set up and use Hide My Email in iCloud+ on all your devices - Apple Support

As described there, you should be able to see and manage Hide My email when logged into iCloud, if you don’t have your iPad.

There's nothing to prevent you from using the hide my email address and associated password using non-Apple devices - however, any email that you receive to your hide my email address will only be directly accessible from your Apple devices.

You presumably know the hide my email address - and have likely saved the associated password for your Vinted account within the Passwords App on your iPad (and other Apple devices).

It follows that using an Android phone along with an iPad loses to convenience and flexibility that you would otherwise enjoy of all your devices were of Apple origin. As is, you will need to manually enter the email (hide my) and password on your Android phone - whether you are using a web browser or App.