Season chicken all over with chopped thyme, paprika, salt, and pepper. Set Instant Pot to Sauté setting.
Add oil to pot and add thighs skin-side down. Cook, in batches if needed, until golden and crisp, 3 to 5 minutes, then flip and cook 3 minutes more. Remove chicken from pot.
Add garlic to pot and cook until fragrant, 1 minute. Add water or chicken broth and thyme sprigs, and use a wooden spoon to scrape the brown bits off the bottom of the pot.
Fit Instant Pot with trivet and place thighs skin side up. Secure lid and press the manual setting. Cook on high for 12 minutes and then naturally release pressure.
Carefully remove thighs and trivet. Place back on Sauté mode. Whisk 3 tablespoons of the hot broth (or water) into flour until smooth, then pour back into pot. Bring up to a simmer and cook until gravy has thickened slightly, about 7 minutes. Remove thyme sprigs and season to taste with salt and pepper.
Serve thighs with gravy.