How do I transfer BTC from my Coinbase account to my Android wallet?
Yes, type it in. Or you can copy the address and email it to yourself and copy and paste it from the email. 

There really isn't any easy mechanism in Bitcoin for the person receiving the funds (i.e. your phone) to request the money from the person sending the funds (i.e. Coinbase). There is the BIP 70 payment protocol but that requires both a compatible wallet on the sender's side and some webserver setup stuff on the receiver side. Even with that, there isn't anything for the sender to initiate the transaction at all, only the receiver.