AFAIK, the G2's definition of "slow charging" is any time it isn't getting (close to) a full 2A from the charger. This doesn't mean the phone isn't charging, or that it's going to take an excessive amount of time to charge. Other chargers will work fine. The Snapdragon 800 CPU supports fast charging, but the opposite of that isn't necessarily "slow".
One thing to watch out for is temperature. If the phone/battery is warm, unplug it for a little while, and maybe even turn it off to let it cool down. If it's too warm, it won't charge very well. I found this out the hard way recently when I left it on the original charger overnight, and it still hadn't gotten to 80% by morning.