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I think that a bit more information is needed here.
Is J1 the MCP4261 ?
The pinout shown for J1 does not match the pinout for the MCP4261. but if you are connecting the pins as numbered to the MCP4261, that should be OK.
What is the MCP4261 being used for?
To get your LEDs to light the resistance will have to be very low. If you write 1 to the resistance value then it will be 40Ω and a current of 3/40 = 75mA will flow. This will destroy your LED(s)- assuming normal 20mA ones. A setting of 4 will reduce the current to less than 20mA and your LED(s) will survive. However, the chip will be dissipating 1/4W - assuming both resistors used. And, that is why it's getting hot. You cannot drive LEDs directly from these devices.