Tinned copper for SPI?
Your system has wires serving two different purposes, though likely the same physical type of wire can be used for both.

What is running at "3 MHz" is the data signalling, which should require relatively modest current, really just to drive the characteristic impedance of the line and the input capacitance of the first chip (as the signal sent to the next is then regenerated).  It is true that at a high signal rate, there will be a "skin effect" in the conductor (and associated ground return), however that isn't really a problem, since the current will be low - the thin annular cross section where the current flows will be ample.

The other thing carried in your multi-wire cable is the DC power to the LEDs, but this should change only at a relatively slow rate, so doesn't really have high frequency content and a skin effect.   Hopefully the variation of current required over time due to the PWM of the LEDs is absorbed in local capacitance (otherwise you would have a source of radio interference).

Now, you might still wonder what happens if the same ground wire is providing the return for both the high data rate signal and the LED power.  It turns out this does not make skin effect an issue either.  As long as the wire can be said to be a linear medium (which for practical purposes, is as long as it doesn't get so hot that the conductivity changes substantially), the high-rate data current has no impact on the resistance felt by the slowly changing LED current - the outer ring of copper will carry both data and power return, while the core will carry only power return.

However, the situations are not entirely independent.  Voltage drop in the ground caused by drawing high power currents through it will affect the voltage seen by the data receiver.  Typically that is within the noise margins of digital signalling - though if there were no local power filtering capacitance and the cable were very long, it is possible that the PWM current could cause enough ground bounce to interfere with the data signalling.