I need a bit of practical theory here.
What I want to know is how much current can AMC7135 chips supply to an XML using 4 X 18650s in parallel? How many chips could be used, and what current could be supplied to the emitter. At what point will the four cells no longer be able to keep up and make any more increase in current?
This depends a lot on the cells... Using 4x20R will give you more than 6A, so you could push it to around 6,5-7A if you wanted. But most cells will not be able to get that peak current. If 4x 20R will give you more than 6,5A, it will only be for a very short amount of time.. Everyting above 6A will only be for a very short time. I would probably go for 6A.
The limiting factor you're going to see is really the forward voltage of the emitter, especially with the XM-L2. The four cells will limit sag a bit but you're not going to be too far ahead on max current vs. a good single cell (at startup, although the four cells will hold it much longer).
Direct drive the emitter with the 4 parallel cells then you will know what you could potentially achieve, then add enough 7135s to come close to that amount. You will have some losses but you will get fairly close to the same amount of output you saw DD. My guess is you'll max out somewhere around 6 amps with an XM-L2 on copper.
Slightly less than direct drive for any given set of cells.
LD D1 (18650 4,35V) would be the ultimate in this combo though.. Higher peak current, much higher average current, and much better capacity. Assuming you have a 4,35V charger..
Wow. I thought there would be arguments, but everyone seems to agree at around 6A max. I’ve been playing with those big 46mm AMC based boards, and now I want to go max.
Each board has three sectors which can be joined together or run to separate emitters. I chipped up one sector, so when I tested it, I hooked up one sector to an LED and got around 3.4A. I tested each sector separately at 3.4A and then hooked the whole thing up. So I guess I’m not really getting 3.4A per emitter when I’m running them all simultaneously.
The 4.35v cells would go a bit higher, maybe up to 7A+. If max output is your goal with the high vF emitters then the 4.35V cells like the LG D1 really do stand out. If you take a look at HKJ's charts they are excellent.
Not much to argue about.. We are all basically saying the same here. (Im kinda repeating RMM, which again repeated me)
And we also have charts to back up what many of us have seen.

HKJ have great discharge graphs.. Just compare the two, and take away a little extra voltage from the cells due to sag from resistance in the wires, switch, driver.
20R would almost be a waste, I would much rather stick to NCR18650B for a normal 4,2V cell. Each cell will have a load at less than 2Amps. Again, the LG D1 (4,35V) would be awesome..
You have 4 cells in parallel… you should be able to supply over 4*battery capacity to the LEDs. An SRK can be mod’d to drive 9A to a single emitter (with my custom SRK driver…) And the cell’s are not even being pushed. IMR cells could do a LOT more.
Sure the cells can supply that much current, but the emitter's forward voltage will limit it substantially. I'm not sure what the max draw on a single XM-L2 is even at 4.2V but I'll bet that it's not even close to 9A. With three XM-Ls you can pull 9A easily but with a single XM-L2 I don't think that 9A is possible without a buck driver.
Adding more LEDs in parallel (divides the current between them, which results in lower forward voltage at that lower current) will be a much easier way to max out a 4.2v-limited input than by adding more cells in parallel. There's only so much voltage to work with even with theoretically perfect zero-sag cells, which don't exist in this universe.
I just remembered. The triple I was making with 4P cells give me a reading of over 8A at the tail. The switch fried.
What is this board you speak of?

An attiny 13a has enough current output to control ~40 or so 7135’s. That’s 15.2A. The current you can draw depends on the cells used, whether protected or unprotected(protection pcb has current limit built in), IMR or LiCo, etc. 4p imr cells could easily provide that 15.2A. If you aren’t using an mcu for modes and want to max out then direct drive will give the highest current from 4p cells.

Where does that come from?
It comes in the NAGE single and triple 4 x 18650 light. It also comes in the YUPARD triple 4 x 18650.