is there a reliable source of charging current? I am testing several chargers and cables to find the optimal combinations for a fast charge.

I was so far using CurrentWidget and was getting just a few values, (independently of how much the battery is charged, for several cables and the same charger, as if there was no losses, etc.). I then tried Charging Report which was giving the same value, but also a "Max" and "Avg" one.

I finally discovered that these values most probably come from 

/sys/class/power_supply/battery/current_*


Since in my case Current > Max (1698 vs. 500) and the max current I get is always 1698 mA (and it is always that for a given charger) I have some doubts about the accuracy of the reported values.

Should I trust them?
Please consider these facts before jumping to conclusions:

The latest Fast Charge uses 3 voltages, 5, 9 and 12V. A higher voltage means a lower current thus a lower drop in voltage and losses, hence the whole point of increasing the voltage. If you have a standard 5V USB charger then all of the above has a sense (measuring just the current). However, if you are using a fast charge system, you need to consider the voltage also (if at 9 or even 12V) and not just the current when measuring externally. 

Long USB leads for 5V charging are a no-no. Good quality copper wire is a must for power hungry devices (1600mAH+ devices). Samsung non-fast charge adapters are bundled with short cables (2 feet max) for this reason. The device does not control the remote charge current, it just is limited to what the cable can handle due to resistive losses. This means that to charge the phone correctly you need at least 5.1-5.2V ON THE PHONE SIDE. The charge circuit in the phone and battery are responsible for providing the correct amount of current depending on the battery and limit the voltage on the battery (max 4.3V with HV Li-Po or Li-Ion cells) and cut off the charge when full.

Charge reporting applications are only as good as the hardware used to monitor it. Different phone manufacturers use different vendor charge control circuits or make their own. This means that if this circuit is not provided with a SHUNT where you can physically SENSE the voltage drop across the calibrated shunt thus calculate a precise current, the current is only estimated based on some voltage drop sampling in time and may vary greatly. What you access through the android power supply class is what this hardware reports, and you cannot know if it is a precise value or not based on the above assumptions. You must know what kind of hardware is used in the device you are monitoring else you are walking in the dark. HTC and some other manufacturers use shunt based current detection while Samsung does not (at least not on its S4 S5 and S6 series), the current reported is based on an estimate that is calculated based on a prior measured voltage and its drop in a certain amount of time (usually a sample per second). This is greatly dependent on the battery state (new, old, defective) but it does give a rough estimate of what the current use is, however, it is NO WAY near the precision of a shunt meter. So please be aware of this fact and know that power reporting applications can only handle the data that is given to them by this hardware, there are no exceptions.

Having said this, the only way to be sure of current usage (current, not power) is using a shunt based meter in series with the charging device. If you want to know if your USB cable is good quality or not, you can easily test this by connecting a source Power supply and voltmeter on the output and see what the voltage drop is on the phone side. The higher the voltage drop the worse the cable. An alternative and easy method is using a sensitive Ohm Meter and measuring pin by pin (just the 2 external pins suffice) what the resistance is.
    5V 1A/h = 5Watts. If your cable measures more than 600-800milliOhms (0.6Ohms) it is a very bad cable. This is equivalent to a 0.2Volt drop when charging 1Amp, hence the phone will revert to 500mAH which is fine for standard USB plugs but half of what a 1Amp charger can charge. 

Additional note: a 5V 2Amp charger will charge any phone or device fine if the device requires less or equal to that current. If the device needs a more powerful charger (3+Amps) and it is still a phone or tablet, the charge limiting system will limit that current to what the charger can handle (2Amps) as it will reduce current until the voltage stays at around 5.2V so it will charge but not as fast as it should. For ex. use an old 5V 700mAmp charger with an S7 will work, but it will take much longer to fill up the 3600mAH battery than with its original Fast Charge charger.

Fast Charge note: Fast Charging is only beneficial when the battery is under 60% charge (50% on some models). When the battery is over 60% it won't be charged at or near its Capacity rating (less if its over the Charge rating) as this will limit the battery life (this has been discovered over years of testing with Lithium Ion technology). The last 10% of charge (so 90% SOC) is well under the rated capacity current as keeping a cell charged too much for too much time will eventually lead it to dehydrate its Hydrogen and expand (bulge). It is best not to discharge Lithium Ion batteries under 40% and not keep them charged for too long over 90-95%. This explains why in recent phones the charge of the battery is sometimes reported 100 but can drop quickly to 95 after disconnecting it, it is merely a safety precaution to prevent overcharging and no defect.

All these things may not appear straightforward, and in fact, they are not for the not privy. Suffice to say that it is a long studied and rather intricate discussion. Charging phones is much more to what meets the eye as there are several components involved and not just the battery itself. It depends mostly on the hardware (phone brand) type of battery (Lithium Ion or Lithium Polymer), charging circuit (phone side and battery) and lastly USB cable used and charger quality and type. Keep all these things in mind when you want the best from your phone's battery life and safety. There is also a difference with sealed phones and user replaceable/removable battery types. This is part of legislation for safety precautions - but this is another story.