You should not glue the pad and carpet together and then glue it to the vinyl as this would cause too much work if it ever needed to be removed.
Vinyl flooring over carpet pad.
Given that most vinyl recommend no rubber here are our non rubber alternatives.
Since there is no rubber in this rug pad it does not prevent slipping.
You can lay vinyl flooring over it.
This is also wrong.
The recycled felt rug pad can be used under rugs that do not tend to slip.
Most vinyl flooring manufacturers recommend using a non rubber product while some will recommend using only rubber.
Just be aware that any bumps or unlevel spots in the linoleum will be seen with a sheet vinyl over top of it.
If you reuse your thick carpet padding your floor will be too bouncy and it may damage the locking system.
The best choice for a rug pad under a rug on a vinyl and linoleum floor is a recycled felt rug pad or natural rubber rug pad.
This pad should be laid down right over the vinyl but not over the carpet runners.
Rug pads for vinyl and vinyl plank floors.
For better results you can use a carpet pad under the carpet.