The order I do these in for a desk back

Thoracic first, always. Skip straight to hip flexors and you're just stretching around the actual problem. (modify as needed)

Cat-Cow

Wakes up the spine before anything else. 10 slow reps, not fast ones.

Open Book Stretch

Foam Roller Thoracic Extension

Prone Press-Up

Push up from the floor, hips stay down. Undoes an hour of slouching in about ninety seconds.

Thread the Needle

Doorway Pec Stretch

Your shoulders round forward because your chest is short, not because your back is weak.

Wall Slides

90/90 Hip Stretch

Couch Stretch

The one everyone skips because it's uncomfortable in year one. By year three it's fine.

Pigeon Pose

Breathe first, don't force the front leg flat.

Glute Bridge

Deep Squat Hold

Two minutes if you can get there. Most desk backs can't yet, that's the point of the rest of this list.

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