How do we say $n$ to be degree of an equation,
We have $F(kx,ky)=k^{n} F(x,y)$ then we say n is the degree of the equation but we generally consider the degree to be the highest power of a variable in a polynomial but here the $k$ is an arbitrary constant so how do we determine the degree of the equation with k?
You have to take into account the fact that you are dealing with two distinct concepts of degree here. You have defined the degree of a polynomial, but the concept of degree of a homogeneous function is a different concept.
Take, for instance, $F(x,y)=x^3+x^2y+xy^2+y^3$. Then, if $k$ is any number, you have\begin{align}F(kx,ky)&=k^3x^3+k^3x^2y+k^3xy^2+k^3y^3\\&=k^3\left(x^3+x^2y+xy^2+y^3\right)\\&=k^3F(x,y),\end{align}and therefore $F$ is a homogeneous function of degree $3$.