H-Bridge motor driver not working properly
When the duty cycle of my PWM signal is set to 50%, the chip only
  draws 0.030A of current, in that case the resistor of my magnetorquer
  would be R=V/I = 2.5/0.03 = 83.33Ω! Which is almost thrice of what is
  stated in the link above!


If you have a 50:50 duty cycle, the average voltage applied to the device is 2.5 volts and 2.5 volts divided by 30 ohms (resistance of the device) is a current of 83 mA BUT, because power-in roughly equals power-out, the current taken from the 5V supply will be half of this at about 40 mA. So you measure 30 mA - it's not too far off and might be explained by slightly incorrect assumptions about duty cycle, measurement errors and metering errors.


  I get on the oscilloscope is a square wave that has max and min
  voltages of 2.5V and -2.5V respectively. If Pin 5(OUTB) of my motor
  driver is always 0, I should expect to see my output voltage vary from
  0-2.5V right?


You've probably got your scope set to measure AC not DC.


  Also, when I set the duty cycle to 100%, I should be expecting to see
  5V on my oscilloscope, but what I see is a very small DC voltage (
  about 100mV ) which is effectively 0.


Yup that's what happens when you have the scope measuring AC.


  I have also tried connecting a the second channel of my DC power
  supply ( Set to 2.5V ) to pins 6 and 7 (InB and InA ) of my motor
  driver chip, when I do this the current jumps up to about 0.150A and
  doesn't increase when I increase the supply voltage of the second
  channel of my DC power supply.


I have no idea why you would do this.