Slice the chicken breasts into 1/2-inch wide strips and pat them dry.
Season the chicken strips evenly with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Set up a breading station: place the 1/2 cup flour in one shallow dish; beat 1 large egg with 2 tablespoons milk in a second dish; combine 3/4 cup shredded coconut and 3/4 cup breadcrumbs in a third dish.
Dredge each chicken strip in flour, shake off excess, dip into the egg mixture, then press into the coconut-breadcrumb mixture to coat completely.
Heat enough vegetable oil in a skillet over medium-high heat to shallow-fry (oil should reach about 350°F or be hot enough that a breadcrumb sizzles on contact).
Fry the coated chicken in batches, without crowding, until golden brown and cooked through, about 3–5 minutes per side depending on thickness.
Transfer cooked chicken to a paper towel–lined plate to drain briefly, then serve immediately.