Is this Corrected Mass Flow equation correct? I have an engine air mass flow rate (322 kg/s) which I would like to convert to a corrected mass flow rate at 10000 feet.

I have tried using the equation found here. However, this article lacks any sources and I have struggled to find any other reliable sources online. 

I have made an attempt using the equation in the article but have gotten a greater mass flow than 322, which doesn't make sense.

Is the equation in the article correct or am I just calculating this wrong?

For 10000 ft I get:

Temperature 268K
Pressure 69.6817 KPa

So
Theta = 0.9301 and Delta = 0.6877

Which gives a corrected mass flow of 451 kg/s.
The equations on Wikipedia are correct (see Flack, for example). I believe your error is in their interpretation. You say that you are given a mass flow rate and want to "convert [it] to a corrected mass flow rate at 10000 feet." But the direction you take the equations is as if you have a mass flow rate at 10000 feet and want to convert it to the mass flow at sea level. If the latter is what you intended, then I see no error. If the former, you need to invert the equation.