In a large skillet, heat oil over medium-low until it reaches 375°F.
In another skillet, cook the ground chicken with minced garlic and ginger over medium heat, breaking it apart as it browns. Season with salt and pepper.
Once the chicken is fully cooked, add the shredded cabbage, carrots, and green onion. Stir-fry the mixture for about 5 minutes until everything is heated through. Set aside and remove from heat.
Mix together the flour and water in a small bowl to form a thick paste for sealing the egg rolls.
Lay out one egg roll wrapper on a clean, flat surface with a corner facing you. Spoon about 1/4 cup of the chicken and vegetable filling into the center. Fold the bottom corner over the filling, then fold the sides in, and roll tightly. Seal the top corner with the flour paste. Repeat this for all the wrappers.
Gently place 2-3 egg rolls into the hot oil at a time, frying for around 2 minutes. Use tongs to turn the rolls until they are evenly golden brown.
Once fried, transfer the rolls onto a paper towel-lined plate to drain excess oil.