If I have a 10A and a 20A power supply is it possible to wire them together to get 30A of output?

No

+2 No!! Purchase a P/S that suits your needs.

Thanks for the reply. What do you guys think of the converted pc server power supplys. I am looking at one on eBay that is 900w and 75A. My charger is only 400w/20A so I feel like this should be more than enough headroom for the power supply.

You can calculate what you realy gonna ask from the power supply.
If the charger is max 20A and you will charge 2S batteries it will ask 170 watt.

But yes, those server PSU's are well used for RC chargers....

I have a 47 amp 12.5v server supply i use all the time ..some what quite .. I also have a 74 amp server ps and it is LOUD like a bees nest..Both are good even when maxed..The 20 amp you have already should suit your needs.

Look at the HP600 power supply, and nothing wrong with computer power supplies. I can run two chargers off mine, 250 and 300 watt chargers, 10 and 20 amp, no problem. As far as wiring two power supplies, you would have to disable the ground on one, and wire it to the other. Not sure if parallel or series? But, you better know what you are doing!! The 900 watt power supply is easy to mod as well, only needing a resistor wired in. There are forums that tell you how to do it, and it is very easy to do. I have three of the HP600's modded right now, and all work well, 575 watts, 12.5 volts, and 47 amps each, not bad.