You can install Eco Cork Foam directly onto the concrete floor. Moisture vapour barrier facing up.

Note that you should check your concrete floor for moisture and ph level.
If you have cracks on the concrete this needs to be fixed.

If you do have concerns of moisture coming through the concrete floor than a subfloor is the best practise - check Dri-Core an excellent product in forming a subfloor. If you do use such a product than the Eco Cork Foam moisture vapour barrier needs to be installed facing up.

It is a misconception that a mositure barrier is not reqquired above grade on concrete subfloors. All subfloors that are concrete whether below grade, on a main floor including high-rises (condominiums) in all floor levels requries a moisture barrier. All concrete subfloors have moisture and Ph factores to consider so it is highly recommended to have the subfloor tested for moisture and PH levels prior to installing any type of flooring to make sure it does not exceed the flooring covering mfg specific quidlines. You will notice that most lamiante and engineered flooring manufacturers recommend and or require a true moisture vapour barrier to uphold thier warranties on concrete.
It is most important that the mositure vapour barrier meets the National Sandards of Canada (CAN/CGSB-51.34-M86) in specific thickness and construction - such as the barrier that comes with Eco Cork Foam. When using building materials in your home that meet building code standards you will enjoy the comfort of knowing that any potential home insurance claims will be better covered.
As a footnote, never install a secondary mositure vapour barrier underneath or on top of an underlayment with a plastic film sheeting of any thickness as it can casue mosture in between the two plastic sheets.

In fact Eco Cork Foam can be used with hardwood floors and many contactors have done so.
What is needed is the correct nail lengths to reflect the needs of the thickness of the wood floors and Eco Cork Foam's 3.2mm thickness. Nails are preferred over staples.

It is not necesaary to glue-down Eco Cork Foam to a concrete sub-floor. If you decide to do so, alwasy install with the mositure vapour barrier facing down, the sub-floor. Also, use the correct glue which is avialble at Home Depot Canada and make sure to follow glue instructions - allowing glue to breath (become tacky) before installing underlayment.

The package claims an R-value of 3.1. This is an utter fabrication.
Cork has an R-value of between 3 to 3.6 or so per INCH. Eco Cork Foam is 1/8" thick. That means its effective R-value is more like R 0.4. I suppose they were saving ink in printing the package (and electrons in the website) and left out the fact that the R-value is 3.1 "per inch of thickness". Note I am using U.S. customary units here. If we were using SI units, the R-value would be about six times smaller.
For Eco Cork Foam to actually have an R-value of 3.1, its material would need to have an R-value rating of 24.8 per inch. To give a comparison, EPS foam has R-value of about 4 per inch, silica aerogel is about R10 per inch, and only vacuum insulated panels have effective R-value of 30 to 50 per inch.

The manufacturer's instructions in the package suggest not to do this. The reason is because the Eco Cork Foam product has a vapour barrier bonded to one side. With 2 layers, you'd end up with at least one layer of cork trapped between 2 layers of plastic. This will likely lead to rotting of the cork over time, as you'd end up with moisture trapped there.
Putting the 2 layers of cork outside isn't any better, as you want the plastic towards the wood flooring.
If you're looking for better acoustic performance, you'd be better off adding a thicker built-up subfloor (plywood & something dense like XPS).

There is no need to duct tape them together. Lay it foam side down with the plastic vapour barrier up. But the two strips together, remove the paper from the self adhesive strip and fold over the vapour barrier flap from the previous strip, Once the laminate covers the seam, your vapour barrier will be air tight.