The problem of building a proper power supply for the Raspberry has been discussed at lots of places, and the canonical answer is to buy the official Raspberry power adapter.
I just bought one myself, price was not too high, something like 14 euro, and this includes a contribution to some charitable projects. It is rated 5.1 V and 2 A, and has pretty thick copper wires to the usb plug. It powers the Raspberry including the touchscreen monitor without showing any of those nasty lighting bolt icons.
As for the maximum allowable voltage: I did not yet measure the exact output voltage of this adapter, but it appears to be within the USB spec of 5 V +/- 5%, i.e. 4.75 - 5.25 V DC. It is with 5.1 V slightly higher than the 5.0 V rating of regular usb chargers.
Hence there is no need to try higher voltages than the official usb voltage spec of max 5.25 V.
In fact, your lightning bolts are not shown because the rated voltage is too low, but indicates that the minimum voltage is below some threshold. The voltage may be sagging at moments of higher currents, and those voltage sags are not that easy to measure. You need at least an oscilloscope. Those voltage sags may also be very short, milliseconds to microseconds.
The current rating of the power supply is also not very important, as the actual load, even with monitor, is well below 1 A. One may expect that a higher current rating may help prevent voltage to sag too much, but I have tried several usb chargers rated 2A, 2.5A and 3A, that still cause lightning bolts to show. USB chargers are designed to be cheap, not to power a raspberry pi.
As the official raspberry power adapter is rated 2 or 2.5 A, you could try to power more than one raspberry pi from one adapter. It would be interesting to see if the lightning bolts reappear. If so, you should ignore the current rating, and use it to power only one pi.