Relationship between feature maps of othogonal kernel functions

Question

So imagine you have 2 kernel functions $K_1(x,y)$ and $K_2(x,y)$ that are orthogonal. By Mercer's theorem they also are defined by an inner product in some feature space mapped by a feature map $\phi$. i.e. $K_1(x,y) = \langle\phi_1(x),\phi_1(y)\rangle $ and $K_2(x,y) = \langle\phi_2(x),\phi_2(y)\rangle$. Given $K_1(x,y)$ and $K_2(x,y)$ are orthogonal what information can we gain about the relationship between $\phi_1(x)$ and $\phi_2(x)$?