Dry short ribs and season generously with salt. Add olive oil to pot and swirl to coat. When smoking, add short ribs, in batches, and saute until deeply golden brown, about 5 minutes per side.
Remove ribs to a plate as they finish and replenish or drain oil as necessary to maintain approximately 2 tablespoons per batch. Return all ribs to pot, sprinkle with flour and toss to coat.
Add wine and reduce by half, about 8 minutes, scraping bottom of pot to deglaze. (This can also be done in a skillet over high heat. Saute timing will be reduced. Transfer ribs and pan sauce to Instant Pot before proceeding.).
Arrange ribs in as even a layer as possible and disperse carrots, celery, leeks, garlic, bay leaf, and red pepper flakes throughout. Add broth, bring to a simmer, and top with fingerling potatoes. Season all vegetables generously with salt and pepper.
Top with lid and place on high pressure. Cook 45 minutes and then allow pressure to release naturally for 30 minutes. Uncover and remove ribs and vegetables with a slotted spoon. Tent with foil to keep warm.
Transfer cooking liquid to a fat separator or measuring cup and skim fat. If desired, return sauce to Instant Pot and reduce to desired consistency. Season sauce with salt and pepper.
Serve ribs with potatoes, vegetables, and sauce, garnished with herbs.