What is the maximum amperage on the 15 volt side for the Pro-ject Power Box ds2 Sources

The way to tell is to power your turntable and measure the voltage under load.  If it stays at 15V, you are good.

The root of my inquiry is that my turntable requires 15 v DC/1.6 A. 

The root of your problem is a misunderstanding of amperage. The turntable does not require 1.6A, it draws 1.6A. That is to say it will run just fine on a power supply capable of delivering 1.6A or greater. You could connect it to a power supply capable of delivering 100A, it would not hurt a thing. The table only needs 1.6A. That is all it will draw.

This is different than voltage. Voltage is pressure. Too much voltage, then you would have a problem. High enough voltage would simply arc right through everything in its path. 

Its like trying to drink out of a fountain. If the current flow is low it just takes longer to quench your thirst. But if the voltage (pressure) is too high its like a power washer and it blows your face off before you can even take a sip.

 I am attempting to power both my turntable and phono pre amp with the same power supply but I have not done so because of not knowing what the maximum amperage is for the Power Box. 

This is a bad idea regardless. The main task of a power supply is to provide a steady source of power. The turntable especially is highly sensitive to fluctuations in power. Normally the turntable motor power needs fluctuate only microscopically due to stylus drag. The power needs of the phono stage however fluctuate dramatically with the music signal. Worst of all, the same dynamic impulse that drags on the stylus calling for more motor power is also almost simultaneously causing the phono stage to require a lot more power. 

It will work. No doubt about it. If the power supply is good quality it will probably only need to be capable of 5 watts or so to work quite well. Until you compare side by side with two good power supplies, only then will you know how bad it was. I'm simply pointing out the technical problems that explain why its not such a great idea.

millercarbon,
your explanation was very good and i now have, I believe  a better understanding of amperage however, I still don't know if the power supply is capable of addressing (for a lack of better terms) the draw of the of the turntable. Again, the power supply does NOT give an amperage rating.  So if the turntable "draws" 1.6A is the power supply capable of supplying 1.6A when he amperage is not stated? Thank you all for your responses thus far. I will probably take your advice and not use the power supply for both but now I'm more curious than anything else about the amperage question.

I appreciate your predicament. Since wall warts are not very expensive, why not avoid the issue by using two discrete supplies? In any case, what erik is saying is that if the PS cannot supply 1.6A of current under the load represented by turntable, the result will be that the DC voltage measured at the turntable will sag below 15V. That might or might not noticeably affect performance of the tt, depending of course on how deep is the sag. If there is no voltage sag, then at least you are not vastly exceeding the capability of the PS. But most of us worthy of the appellation "audiophile" would want to know that the PS potential is in excess of what is needed. If you see 15V and the PS does not get hot or very warm to the touch, then you are nevertheless probably OK.

I realize that to detect a voltage sag, you need a voltmeter and access to nodes on the power input side of the tt where you can assess DCV.  That might be a problem.  In which case, you might just hook it up and let the turntable run for an hour or so while monitoring the temperature of the PS chassis.  If it gets hot, stop.