You must know that soul music is not just about the vocals rather you must have emotions and a unique texture in your voice. First of all, try to catch the feel of music and understand the lyrics before starting the singing.
Pick some album of Alicia Keys and listen to all songs for a detailed introduction to her singing style. Her first album “Songs In A minor” can be really helpful in understanding the basics. Keep listening and try to notice the way she adjusts her voice in different songs.
Pick your favourite song and understand the lyrics as this will really help you to deliver those lines like Alicia did. You can write lyrics on a paper and then sing along with the Diva of soul music.
To make the rehearsal more simple and effective, use an ear phone in one ear and try to listen and sing at the same time. However, you must keep in mind that singing like Alicia Keys does not mean imitating her completely. Do get inspired but you should not lose the original character of your voice.
You should practice scales to make your voice more adept. Mostly, soul singers are expert of the Blues scales so you should practice minor pentatonic with a sharp fourth. You must be able to restrain your vocal chords and keep them taut. Try to hit the notes and hold them for a while. This exercise will really help you to be a quality singer like Alicia Keys.
Buy a Karaoke version of Alicia’s songs and sing along. Play again and again to develop a voice like Alicia Keys.
Record and play your voice again and again. Notice the shortcomings and try to improve your singing. The best thing you can do is to listen Alicia more and more. This will really help you to understand her range and variety.