In a medium bowl, toss shallots with flour. Put in a strainer, shake off excess flour, and transfer to a plate, being careful not to let shallots clump up.
Pour enough oil into a 4- to 6-qt. saucepan to come 1 1/2 in. up side, then heat over medium-high until it registers 350° on a deep-fry thermometer. Add shallots and fry, stirring constantly to keep them separated, until golden brown, 3 to 4 minutes (they will darken as they cool). With a slotted spoon, transfer to paper towels to drain. Season with salt.
MAKE AHEAD: 2 days, stored airtight at room temperature (re-crisp, spread out on a baking sheet, at 350° for 5 minutes).