Can the output of two 15-amp motor drivers be hooked up in series to achieve a 30-amp tolerance?
Short answer: no.

Long answer: maybe but probably NO, because of the following reasons.
First of all you are misusing the word "series": you can't actually connect two of these things in series since they have more than two terminals, anyway if you hook their outputs in someting that might seem "series", and that's not possible since they seem to be full bridge controller, what you would achieve is dobule the maximum voltage rating. You might want to connect them in parallel thus dobuling the maximum output current. That might actually work, but there's some reasons why it probably won't. Have a look at this pic:



source: wikipedia

Assuming you understand basic electronics, the circuit you are seeing is pretty simple: when S1 and S4 are closed the motor spins in one direction, when S3 and S2 are it spin reverse. Since you say you wrote an application that goes from 0% to 100% I'm assuming that you know also what PWM is so I'm just skipping that part.
As you can see from the photos from ebay that's exactly your circuit, the eight big components with metal tabs on theyr back are the MOSfets, four per each channel, and they are used as switches.

So let's say you take two full bridge circuits, A and B, you'll have \$S1_A\$, \$S1_B\$ and so on. Let's assume you hook the node \$S1_A - S2_A\$ to the node \$S1_B - S2_B\$ and similarly with \$S3_x\$ and \$S4_x\$, then you connect your motor just as in the picture and fire up your program. Of course you need to tie togheter the PWM and direction input pins of both the controllers. Assuming you connected all up correctly the corresponding switches should be on or off at the same time, so you have two parallel mosfets, that is good, and they can actually bring double the current. But here comes the trick: there's some sort of circuitry between your control inputs and the mosfet gates, U1,2,3,4,5,6. There also is a step up, but focusing on the MOS driver part we can isolate the problem. These circuits take your TTL or CMOS inputs and translate them in gate volages for the mosfets. These circuits introduce delays, and dealys differ from one chip to the other due to manufacturing tolerances. It is then possible that due to different delays one circuit switch off S1 and S4 and then turns on S2 and S3 while the other is still keeping S1 and S4 on. What do you get? A short circuit on the batteries, which is very very bad. The thing might even work, maybe the short circuit time is so small that the mos can actually carry the current, but they'd get very hot, your motor would be braking (shorted terminals!) and efficiency would be not acceptable. What can you do about that?

Easy solution: try and see if it works. I discourage this because it might work, without proper equipment you can't really see what's happening and you will end up with an unreliable design.

Easiest soultion: find out your motor specs and buy the correct drivers

Tricky solution: that's what you are looking for. The mos driver circuit is aware of the danger of shorting the supply, so when it switches off S1 and S4 it waits some time before switching on S2 and S3. If you provide U1 and U2 codes (can't read them from the photos) I can help you check the datasheets to see if this "dead time" is long enough to let you actually hook up the outputs in parallel and rest easy. As Phil noted this solution is still a bad idea because also if you can be extra sure that no supply short circuit will ever occur it is not possible to switch all the mos at the same time, so there will be (brief) moments in which only one mos supplies all the current, that is twice its maximum or four times the maximum power.