Attach a candy thermometer to a Dutch oven or other large heavy pot, then pour in 3 inches of oil and set over medium-high heat. Heat the oil to 350-375 degrees.
In a medium-sized bowl, stir together the almond flour, coconut flour, baking powder and salt. Stir in the rest of the ingredients and mix until blended. Do not overmix.
Use a tablespoon-sized cookie scoop to gently drop the batter into the oil. Don't overcrowd the hushpuppies; cook them in two batches. Fry for 3 minutes or until the start to brown, then use a mesh skimmer or slotted spoon to turn and fry them for 3 more minutes or until golden brown on all sides.
Remove the hushpuppies from the oil and place on a paper towel lined plate to drain. They are best served immediately.