The unit you bought simply does NOT work for the application you have, and never can.
Your math is wrong as well, so lets start there:
I'll ignore heatsinks, conversion efficiency, circuit configuration etc etc.
Your LEDs require 12V DC @ 21A ---> 252W at full power.
With an input voltage of 4.2V (fully charged cells) to supply 252W you would need to be able to supply 60A from your battery pack.
To achieve your goal you'd need a boost convertor that can supply 252W. The unit you linked to shows little real details, but you can see that it is based on the TI LM2587 IC.
Reference to the chip data shows that the 5A current capability turns out to be the maximum peak current that can be drawn on the INPUT side. This can be clearly seen from the block diagram, which shows the current sensing for the output switch:
Ignoring dozens of other elements in this design of a boost convertor, for you this indicates the absolute maximum input power could be 5A * 4.2V --> 21W (you can't actually ever get close to this for some of those other reasons, but I'm doing the shorthand version to show how far from reality you are).
So to summarize:
The boost convertor will not work for you since it CANNOT provide the power you need, even at reduced illumination.
The boost convertor is the wrong type of convertor to drive your LEDs. While the COB modules you seem to have CAN be voltage driven, you have to sense the module temperature accurately to do this. It is always better to use CC drive.
The battery pack is not large enough to power your LEDs for more than a few minutes even if the convertor would work.
The 0.7A (I assume here you are measuring the LED current) you see is about 8.5W, which is exactly what I'd anticipate in a convertor that is current limited in the way this unit is.
Back to the drawing board and work with some real values.
Perhaps as a starting point you could consider:
- Build a 4SxP or 5SxP battery pack to suite the runtime you need at the current you need.
- Use something like this Buck convertor with one unit for EACH INDIVIDUAL LED. This unit allows the absolute voltage or current to be set (CC/CV) and they work quite adequately for this type of application.
It may also help to read some basic information on the COB LED modules, perhaps start here or here. These modules are a simple series and parallel configuration of LEDs with NO current limiting other than their slope resistance. You need to carefully monitor the current, voltage and temperature of the module to get long term reliability.