What is the physical relationship between current (I) and magnetic flux density (B)?

Referring to the magnetic field produced by an electric current (only one of the possible ways of interpreting this question), the Biot-Savart law provides a non-relativistic approximation: "In the special case of a constant, uniform current I, the magnetic field B is

B = K_m I int frac{dmathbf l imes mathbf{hat r}}{r^2} "

The mathematical symbols don't copy nicely! The magnetic flux density is proportional to the steady current, but varies as you move away from the conductor in whoch the current flows.

https://en.wikipedia.org/wiki/Biot-Savart_law

If you refer to the current induced when a conductor moves through a magnetic field, then the induced emf is proportional to the rate of change of the magentic flux with respect to time (Faraday's Law); assuming an ohmic conductor, the current will be proportional to the emf; if the magnetic field is uniform, magnetic flux is proportional to magnetic flux density so I is proportional to dB/dt. (This is a vastly-simplified situation, but the mathematical symbols needed to show a more accurate answer are hideous when copied here!)

https://en.wikipedia.org/wiki/Electromagnetic_induction