Recently, my student Chloe had oral surgery which will keep her from actually playing her flute for about 6 weeks. Her mother wisely decided to keep her in flute lessons during her recovery time, so I was pleased to have the opportunity to help Chloe learn how to practice "away" from her flute.
Sometimes it is even more helpful to practice without an instrument than with it because it reduces distractions and helps us to focus on specific concepts we are trying to learn. It is easy to fill a 30-60 minute or more practice session developing rhythm, breathing, theory, and even technical passages. In Chloe's lessons, we work from a rhythm book for the first segment anyway, so we check the written counts and then clap out rhythms. If the tempo is inconsistent, we use a metronome. To change things up, I might even use a percussion instrument to perform the rhythm exercises.
Chloe doesn't want to get behind in learning her music, either, so we use her flute to finger the music and "air play". If we listen carefully, we hear the pitches that are voiced when the flute keys are depressed because the flute tube resonates quietly. That way, we do know if she's hitting the right notes. She gets used to the note combinations without having to blow! This exercise is one I commonly use in other students' lessons as well: we call out the note names (in rhythm, of course) while synchronizing the key fingerings. The brain makes a strong connection when so many kinesthetic tools are used: feeling the fingering, saying a note name, hearing oneself call out the note name, etc.
While playing "air flute", it would be easy to forget to breathe in appropriate places because air is not used in the same way. Therefore, it is important to consciously inhale at the breath marks just as one would do while playing. Building this habit is quicker than trying to learn many things at once, as when one is sight reading or learning a piece in the beginning stages.
When Chloe is able to resume regular flute playing, I fully expect that she will not have lost any ground. In fact, some habits may be stronger, and others may have improved! Practicing "away from the flute" is handy for all students, whether they are in a place where they are not allowed to make much noise, such as while waiting in band class, or if they want to learn a concept quickly by building one habit at a time.