How does recovery key work?

Do you have 2 Factor Authentication or 2 Step Verification enabled?

See if anything here helps.

Apple ID -Two-factor authentication          

2 Factor Authentication - How to generate a recovery key  

Apple ID - Two Step Verifications FAQ    

The Recovery Process is an automated process and the length of time it takes can vary a lot. Apple ID Support can only answer your questions. They can't intervene in or speed up the process. The article below has some suggestions to shorten the the time the process takes.

Apple ID - Recover your Apple ID with two-factor authentication account recovery.   

Hi, i have two factor authentication enabled but i no longer have the phone number i used to register it. I have tried the recovery but it says 6 days until I’m able to change phone numbers. Any chance i can get it sooner?

See the options in this link.

Apple ID - Password/Security Questions verification e-mail not received.