To write a Java program for finding the nth multiple of a number in the Fibonacci series, we can follow the steps below:

1. First, we define a function that takes two integer arguments, n and k, where n is the index of the multiple we want to find, and k is the number we want to find multiples of.

2. We initialize two integer variables, a and b, to 0 and 1 respectively, as these are the first two numbers in the Fibonacci series.

3. We then loop from 2 to n, calculating each number in the Fibonacci series by adding the two previous numbers, and storing them in a and b.

4. Inside the loop, we check if a is a multiple of k using the modulo operator (%). If it is, we decrement n by 1. When n reaches 0, we return a.

5. If a is not a multiple of k, we continue the loop until we find the nth multiple of k in the Fibonacci series.

Here is the code for the program: 

public static int nthFibonacciMultiple(int n, int k) {
    int a = 0;
    int b = 1;
    for (int i = 2; i <= n; i++) {
        int c = a + b;
        a = b;
        b = c;
        if (a % k == 0) {
            n--;
            if (n == 0) {
                return a;
            }
        }
    }
    return -1;
}

This function returns the nth multiple of k in the Fibonacci series, or -1 if there is no such multiple.