Mix flour, salt, and pepper together in a shallow bowl.
Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select Saute function. Add 1 tablespoon olive oil.
Dredge 4 chicken thighs in the flour mixture and shake off any excess. Saute until golden brown, 4 to 5 minutes per side. Transfer to a plate. Repeat with remaining 4 chicken thighs.
Heat remaining 1 tablespoon oil in the pot. Add onion. Cook and stir until translucent, 4 to 5 minutes. Add garlic and cook just until fragrant, about 1 minute. Pour in wine and scrape the browned bits of food off the bottom of the pot with a wooden spoon. Continue cooking until the wine has almost evaporated. Add tomato sauce; stir in oregano, basil, parsley, red pepper flakes, and bay leaf.
Return chicken thighs to the pot and turn to coat with sauce. Close and lock the lid. Close the vent. Select Chicken function; set timer for 10 minutes. Allow 15 to 20 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove lid.