Could we connect two 5 Volt phone chargers of different ratings in parallel for quick charging with a diode as shown(rectangles being the chargers)
Please excuse me for the drawing I made..
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The voltage drop in the diode will make the voltages in the two chargers unequal(as if they already weren't), and one charger will probably carry more current than the other, that one will hit its current limit and might shut down to protect itself. If you leave the diode out of course there might be a short. Paralleling these is generally a bad idea(series on the other hand is a less bad idea with isolated power supplies, but that doesn't help much here)
It might appear to work, but one charger will be pushed to 100% or more, there might be EMI/noise issues, and chargers are too cheap to bother with. And besides, old chargers are great for all kinds of things :)
You might be able to use resistors of just the right size to share current accurately, but why bother?
If you had a 5V supply as the power source for a charging circuit, the current drawn would be determined by the circuit being charged. If you connected in parallel two 5V power sources, the current drawn would be exactly the same and therefore no net benefit.
If you put diodes in series with the two supplies you would get maybe 4.5 volts and the charging circuit would not be good at all.
If, however, on the other hand, the power supplies were constant current types then paralleling two supplies could give twice the current BUT, if the constant current power supply is specifically intended for the battery why would you try and charge it at twice the rating? This might damage it.