The teeth are not involved in the bilabial (two lips) /p/ sound. In 'slurp from', your lower lip should move back from the /p/ position to make contact with your upper front teeth for the /f/. You cannot produce a /p/ sound by biting your lip. You can produce a /f/ sound in this way, but it's not necessary to do this. If there is a gap between your lips when you are trying to produce a /p/ then you are not producing a /p/.
Note that the /p/ is not fully released when you say 'slurp from', so you will not hear/feel the aspiration (release of air) you would if you said 'slurping'.