Certainly providing accurate enough measurements is not s trivial task!! In addition, creating a stable measurement system is seldom simple or cheap. And the influence of external conditions is always a challenge. Those are the realities of providing accurate measurements of physical quantities.
The good news is that much of the time "extremely precise" is not required, unlike "Rocket Science", which needs to be exact.
A large amount of engineering involves knowing how "close enough" needs to be to meet the requirements in a satisfactory manner.

For measuring currents there are a large number of guide-lines that allow avoiding many of the external variables that are seldom small enough to ignore. Some are well known but not intuitive, others, it seems, must be learned by each individual.

I think that I have seen even within these forums, another article on measuring and even controlling model rocket igniter current. So a bit of seeking in this realm might show how to get the answers you seek.

 

I am seriously baffled,
why such a complex pile of Chips and Circuitry for a Rocket-Igniter ?????

Do You want faster response-times ?
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My take on the post is that the TS was hoping to learn enough to be able to develop a more compact and more effective igniter device. While the igniters that I am familiar with are intended as single use items, there exists a lot of room for improvement in both performance and reliability.
So really, the TS was trying to create a research/development tool.
The non-hobby igniters that I am familiar with mostly use an exploding-bridge-wire arrangement. More durable and much more predictable. And safer as well.

 

@MisterBill2 is correct. If all I wanted to do is launch a rocket, all I need is a batter, some wire, and a switch.

My rocket launcher project is a little more than that - a cell phone for wireless communication to the launcher so no wires across the field, small launcher box with rechargeable battery at the launch stand so there can be multiple launch stands as needed. Version 1 is "in production" and is working as expected. I am working on version two to reduce component count and battery size.

Just to be clear, this is not a commercial venture. As a volunteer, I have been teaching rocketry to fifth graders at my local elementary school for the past 24 years, and this launcher is just for my use. A fun project to get back to my EE roots from many many years ago.

I am trying to measure the current with some degree of accuracy so I can correctly size components to meet the needs of the igniter and have the smallest launch box and battery at the stand.

The last technical evaluation of igniters was published in 2000, and they have changed a lot since then. That analysis demonstrated igniters need 10A for 500 msec to ignite. My tests have shown the StarTech igniters only need 2-3 amps for about 200-300 msec. There is a trade-off between current and duration as the current is just heating up the igniter wires (usually nichrome, but that has been changing with newer igniters) to the flash point of the igniter material, which use to be pyrogen, but that is also changing as igniters evolve.

Sadly, my SD card died after my last set of tests this week, so I am waiting for another one to continue my evaluaitons and design iterations in the quest for more accurate current measurements.

 

If I can offer a comment, which is that the correct explanation of how the launcher functions is much simpler for the package with the wires, battery, indicator light, and push button switch. The ten amps for 500 milliseconds seems closer to the exploding bridge-wire scheme, but maybe not. For the older hot-wire scheme, I was the one who could re-use the igniters by pushing them into the ESTES engine and then scraping off a match head for the flash powder. They always worked so it must have been close enough. I never tried it with a Claymore, that was a whole different game.