Place flour in a bag, add onions and shake to coat evenly with flour.
Pour oil into a deep 2-1/2 to 3-quart pan to a depth of 1-1/2 inches and heat to 300ºF. Add floured onions, about a fourth at a time, and cook, stirring often, until golden brown (about 5 minutes). Oil temperature will drop at first but will rise again as onions cook; regulate heat accordingly.
With a slotted spoon, lift out onions and drain on paper towels (discard any scorched onion bits). Serve warm, piled in a napkin-lined basket or in a warmed bowl; sprinkle with salt.
If made ahead, let cool, wrap airtight, and refrigerate for up to 3 days. To reheat, spread onions in a single layer on a shallow rimmed baking sheet. Heat in a 350ºF oven for 2 to 3 minutes.