To make the dressing, thinly slice 2 shallots and separate into rings. In a self-sealing plastic bag, toss sliced shallots with flour, 3/4 teaspoon salt and a large pinch of pepper until well coated. Shake any excess flour mixture off shallots and transfer them to a plate.
In a 10-inch skillet, heat 6 tablespoons olive oil over medium heat. Add sliced shallots in batches and cook, stirring, until golden brown and crisp, 2 to 3 minutes. Remove shallots with a slotted spoon; drain on paper towels.
Mince remaining shallot. In a small saucepan, heat remaining 2 tablespoons olive oil, minced shallot, lemon juice, thyme, remaining 1/4 teaspoon salt and a large pinch of pepper over low heat; cook 1 minute, until just warm. Pour dressing over arugula mixture and toss well. Sprinkle with crisp shallots and serve warm.