Many of Illegal Immigrant have flown within the U.S. without incident. The risk is greater. To board an airplane, all travelers must present a government-issued ID.
A foreign passport meets that condition. Of course, if migration officials review your papers you could be detained.
Though, if you are in removal proceedings you could travel. You will need to produce your (1) Notice to Appear (Form I-862) issued by the Executive Office of Immigration Review; and (2) your ID (even foreign passport).
If you are delivered a Notice to Appear it means that you have already been interview by immigration officials plus they have started proceedings to deport you from the U.S. They usually have no cause to detain you, again.