Touch the front of your tongue to the roof of your mouth, then release into a 'sh' position. Flare your lips.

Americans pronounce chirp as CHURP (/tʃɜrp/). You'll hear it in sentences like "The girl heard the bird chirp firmly".
Record yourself saying "chirp" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 3 sounds. Explore each sound's mouth shape and how it's made.
Touch the front of your tongue to the roof of your mouth, then release into a 'sh' position. Flare your lips.

Flare your lips and push them away from the face. Lift the middle of your tongue toward the roof of the mouth.

Press your lips together to stop the air, then release. No vocal cord vibration.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "chirp", the "p" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Americans use a relaxed retroflex R — the tongue curls back rather than rolling. The R is one continuous sound with the vowel before it, not two separate sounds.