I would think that high silica flows do not actually "flow", but tumble like a pile of boulders and gravel living gaps between them. When the pile gets thicker the weight of the overlying rock will create cracks to add to the overall permeability of the ground.

I agree. Yet the 6300m Chimborazo volcano, another stratovolcano, that errupted thousands of years ago had produced some 30km long lava flows, which can be seen at the city center of Guano, Ecuador, and keep flushing out 100+ l/s of groundwater that far. On the other hand, lava flows in Apurimac/ Ayacucho are not that obvious, nor visible. I assume all those are stratovolcanos, because of subduction-originated tectonic activity. Am I right?

I found the method proposed by Asai et al, (2009) very interesting. They  describe and model groundwater flow system within an andesitic stratovolcano through water Isotopic chemistry. Asai et al. also proposed some general conclusions about the discharge of groundwater housed within lava flows which can be extrapolated to other volcanic contexts:

http://onlinelibrary.wiley.com/doi/10.1002/hyp.7185/abstract

There could easily be many ash tuffs within these rocks, and when the glassy ash devitrifies it can have enough feldspar such that it degrades and creates a good porosity.  Maybe there are also coarser breccias and tuffs that have higher porosity too.

In a stratovolcano, the majority of the edifice is typically fluid saturated (see Day, 1996). As such, it doesn't necessarily take much by way of subsurface thermal or mechanical strain to increase the pressure of interstitial pore fluids, which could explain your high observed flow rates. A great example of this from Krafla, Iceland, is discussed by Elsworth and Voight (1992) and Elsworth et al. (1996). Moreover, any process which could decrease overall edifice permeability--such as hydrothermal circulation, thermal expansion and closure of cracks, or even just gravitational spreading and compaction--could similarly increase fluid pressures and hence increase flow rates at proximal springs. 

The precise cause will obviously depend on the particular mechanisms at play in the system, the height of the water table, and so on. If you are interested, I could direct you towards a few papers concerned with fluid pressure change in volcanic edifices.

As I understand, the main question is: What is the source of water? Many volcanoes produce a lot of hydrogen and less oxygen, even in their quite period, which are coming strait from the mantle and are not contained in the magma. Reacting, they would produce juvenal water and heat. Are there suitable infrared anomalies shown by low-flying satellites? Or aerial photographs on the infrared-sensitive films? Are there any pluton-related peculiarities in the chemical composition of  those spring-waters,  especially in a dry period?  

Thanks a lot to all of you, for providing very interesting references. Even my minimal geology background allowed me to understand the stratovolcanic fracture formations with pore pressure build-up and other factors during eruptions.  That also may explain the existence of large groundwater storage in these areas.

All the springs I cited are from long dormant volcanos, with little thermal activities nearby and the water quality is good enough for irrigation.

In these areas, very little basic hydrogeologic investigations have been done, nothing at all with isotopes. As for ascertaining the origin of their water source, the farmers have ingenious ways: if your spanish is decent, you would enjoy this 2 minute video:

https://www.youtube.com/watch?v=jAM7s8HeZag

where people dumped tiny quinua seeds at the mouth of a fracture to learn where that water goes.

High flow rate of water in springs associated with volcanic rock formation is very common. Deep water circulation which cause increasing of water temperature and than formation of reservoir/ aquifer in hard volcanic rocks,  and  further changes in density of water , cause  of hydrostatic pressure, and return back water movement towards earth through fault/fissure/cracks may cause high rate of flow of spring.

It would be reasonable to think that the water flow is done through cracks solidification, the argument would be valid if the distances were shorter, it is hard to think of a crack expansion extends ten km; think of several aligned cracks could justify a situation, but not the generality. It would, in my opinion, to see the length of the lava flows and study the interface between successive washes, see its extent and consider the flow occurs at these interfaces.

It is common in springs associated with volcanic rocks.Several types of dikes accelerate the groundwater flow along the two sides and may increase the temperatures. The potentials of flow are obviously changed by the increase of heads and the hydraulic gradients along the associated faults , cracks and joints