Ethernet RMII using ribbon cable
The connector has only two GND pins. 



For better signal integrity you'd need GND lines on both sides of the clock line "OSCIN" (which is actually an output from the PHY module), and probably a few more GND lines to reduce emissions. On this pinout there will be some crosstalk between clock and nearby signal lines.

Also there is only one clock line, running at 50MHz (20ns cycle), it is output by the PHY.

When the PHY transmits data it will be automatically aligned with the clock, and if propagation delays are well matched then RX_Data will reach the MAC with proper timings relative to the clock.

However, when the MAC transmits, it does so according to the clock it receives from the PHY, so these signals will reach the PHY with a delay depending on propagation time (ie, cable length).

The PHY has 10ns data setup time to clock which leaves very little margin with a cycle time of 20ns. So I don't think you'll be able to use a flat cable due to propagation delay.