If I have understood your question properly, then I think you want to find the magnetic flux through one loop due to the current through the another one. First of all, finding the magnetic field at the center only is not sufficient, and moreover $B=\dfrac{ \mu_0I}{2R}$ is the magnetic field at the center of a loop due to the current through its own. So, you don't need it anyway.

Now, At each point on the circular plane of one loop you need to find the magnetic field due to the current through the another. But this is a tedious job (See here how the magnetic field has been found at the axis only. But for off-axis points the job is tedious). After that you need to integrate the magnetic field over the circular plane.

If I have understood your question properly, then I think you want to find the magnetic flux through one loop due to the current through the another one. First of all, finding the magnetic field at the center only is not sufficient, and moreover $B=\dfrac{ \mu_0I}{2R}$ is the magnetic field at the center of a loop due to the current through its own. So, you don't need it anyway.

Now, At each point on the circular plane of one loop you need to find the magnetic field due to the current through the another. But this is a tedious job (See here how the magnetic field has been found at the axis only. But for off-axis points the job is tedious). After that you need to integrate the magnetic field over the circular plane.