Rules for Foldable Duffle Bags

To an airline, there are no differences between a duffel bag or a "fixed dimension travel bag" (aka suitcase). The same restrictions regarding size and weight still apply. Duffel bags have their advantages and disadvantages. Some advantages are that you are generally able to "stuff" more things in there and they can squeeze into weird spaces. Disadvantages could be that they might tear at the seams and/or be awkward/tiresome to carry since you would have to hold it in one hand or strap it over one shoulder.

If you have specific questions regarding checking your luggage or having it as a carry-on, it would be best to contact the airline.

I have been using a foldable duffel bag for hand luggage as well as the odd check in for a couple of years now.

Mine is well undersize for checking in, so no trouble there.
It is on the limits for cabin luggage two ways, (with 5 cm/2" spare in the last,) and it has never even been measured for that. It mostly sits happily under the seat in front of me. (Just very little foot space left, I do not need that.)

If you do not over fill your bag, it can be squezed into the measure size thingy and that is allowed. On the other hand, if you fill it till it is ready to burst seams, you will go over the allowed limits and can be told off for that.

When you check the bag in, if it as a strap that can come off, take it off and stuff it inside or in a pocket. If yours has straps that stay on as those in your link, tie them together as well as possible to avoid them getting stuck on something while in the airport or being loaded/unloaded from the plane. The closer they are to the body of the bag, the less chance on things going wrong.
You can tie a piece of string to the handles, one each, and tie those around the bag, in such a way that the handles are wrapped around the body of the bag and the knot is in the middle of the top or bottom.
If your bag has a shoulder strap that does not come off, you can tie it with the same string, add a second and/or third if you feel that helps. So it also sits as close to the bag as you can manage and does not risk coming away.

I have used my bag on KLM, BA and EasyJet, but I have seen comparable bags (to mine and to what you have in your link) on check-in queues in all airports I have been in years. None of them was rejected. I have even seen very cheap duffel bags being used, the kind most of us would just use for storage and not for travel. As long as the staff at the check-in counter feels it is safe for the system, they allow it.

The rules are no different than for any other bag. It must fit within the airline requirements and weight up to the maximum allowed weight. The exact size and weight allowed obviously depend on the flight and class you will be in.

The important is that it can be squeezed into the sizer, meaning that it it fits even though it does not usually have dimensions specified in 3 dimensions. Many do though, such as the one I use. It is a rectangular prism of cloth without any inner frame is is very flexible but if you expand it in all sides, then it will have a width, length and height.