Ok, time to clarify, and play electronics 101, you cannot test the current capacity of a power supply by turning it to amps and putting your leads across + and -, you need a load for 1A, you would look for a 4.7 ohm 10W resistor, plug your multimeter probes into 10A and common, your black lead to negative of the supply, your red lead to one side of the resistor, and the other side of the resistor to + of the supply,
You would preferably at the same time have another meter measure the voltage across supply + and -, a cheaper charger intended for phones will generally have its output voltage just crash down once loaded to 1A,
For your chargers, if you power the chargers in parallel, you just need a supply that can give out 1A per circuit, each charger consumes up to 1A, internally its regulating it to follow the charge curve. for this you have 2 options, buy an AC brick that gives out 5V at 10A, or grab a laptop power brick and a DC-DC converter that can take in the laptop brick output and supply enough amps at 5V,
I would guess the laptop brick option will be the most compact and cheap option, your using 5Vx9A = 45W, assume a rather cheap DC-DC and lets say 52W input (efficiency losses), so a laptop 16V brick capable of atleast 3.25A
Also if you tried to measure the current while your leads where in the voltage position, try and measure a resistance, you may have blown the 250mA fuse for the mA/V/Ohm range.