The suggestions for a full-wave rectifier and filter cap are the hot ticket, that will eliminate the flicker. I'd recommend at least a 1,000uf 35V capacitor for your application. With DC from a bridge, you'll also get more voltage, so the resistor will have to be sized appropriately. Compute the values as if you're getting around 20 VDC from the supply. I'd probably start with a 33 ohm 2W resistor if both strings of those LED's will be in parallel, that will be totaling 240ma.
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