Charging a phone battery does not require precise 5V regulation, so some phone chargers will not maintain 5V under load. I have tested "5V/2.4A" chargers that dipped well below 5V at only a 1A load.
Another potential problem with phone chargers is the micro-USB cable used to supply power to the Pi. The USB 2.0 specification for power is 5V/500mA (0.5A) and that's all some micro-USB cables are designed to deliver. Besides a good power supply you also need a good micro-USB cable to deliver the power to your Pi3B. Look for a micro-USB cable with at least 24 AWG power wires and preferrable larger (lower number = larger wires, so 20 AWG is better than 24 AWG). Shorter cables also have less resistance, so what you want is the shortest micro-USB cable with the fattest wires you can find (or that is practical). Charging cables included with smartphones or tablets will usually be designed for higher current. Here's a post I made awhile back about some of the best micro-USB cables I have used: viewtopic.php?f=63&t=165393
You should be able to run a Pi3B off of a 5V/2A supply, as long as you don't have very power hungry USB devices attached, but the official RPF power supply, which is rated at 5.1V/2.5A with nice fat 18AWG power wires is highly recommended.
My password is the last 8 digits of Pi.