Uhmmm Ok. This is a pretty broad question (I know...it doesn't SOUND broad...but it is a MASSIVE question).

First thing's first....what SUBSTRATE are you working with? Plywood, OSB, Fibreboard, Cement board, concrete slab? We need to start with the basics.

How BIG is this install? Is it a whole home (imbedded into the concrete slab) or simply a small space (like a bathroom or a kitchen)?

I've seen the "nothing" put underneath a mat like this to 1/2" cork being glued/cemented into place and then more cement poured over it and THEN the floor added on top (that made the floor 1.25 inches HIGHER BTW).

And the final question (which you didn't ask). Is the VINYL flooring rated for infloor heating? If so, is it allowed over ELECTRIC? Most vinyl floors have SEVERE restrictions about heat. The electric mats can heat TOO HIGH for many vinyl products. The in-floor radiant heat with the MOST SUCCESS is hydronic heat (oil/water/gel) because it has lower temps and because it is often embedded into a serious subfloor structure (either under poured concrete or installed under the subfloor from the basement or set into channels in a new subfloor surface).

Please check your VINYL flooring warranty/installation manual before moving forward with the in-floor heat. This is a tough one to get right. And it gets really expensive when it goes wrong.

Let me thank you from the get-go since I'm sure you're sharing professional experience. This is all in the planning stages. It will be in a manufactured home so figure OSB or particle board (typical). I'd like to do the whole place, approximately 1200 sq ft. And I'm just now looking at the vinyl offerings available and really appreciate notes on thermal abilities of the vinyl. I'll check into that. I caught the following video that has inspired me in this:
https://www.youtube.com/watch?v=WrCevMuNk5M Thanks for any thoughts.

Wow...1200sf of electric mats. That is an EXPENSIVE proposition. And not just the install costs. I mean the electrical costs to heat the space will be massive.

And then there is the issue of "whole home heating". Are you TRYING to use the in-floor heating system to HEAT the home? Will you have a primary heat source (such as forced air or base board heat)?

When it comes to in-floor heating systems, please be aware the mats are traditionally used as "added warmth" for the toes. They are not normally used to heat the home. A primary heat source normally has to be used to do 95% of the work to heat the home.

When looking at "whole home" heating with in-floor radiant heat, we normally work with HYDRONIC (water/oil/gel filled tubing). The hydronic systems can be used under wood based subfloors. That's not a problem. They do NOT have to be embedded in concrete. They are either set into the subfloor (looks like the grand canyon in your subfloor with a deep valley snaking through the floors) or they are mounted underneath the subfloor from the basement side of things.

The hydronic install is the most expensive (material + install) but it is the most economic (when compared to electric mats) to run. It can be more expensive to run than a high-end HVAC system in a well insulated envelope.

As you can see, the heat mats are not normally used as "home heating". They are considered to be toe warmers. That's it. And they are expensive toe warmers when compared to area rugs and cool socks/slippers.

Just a little FYI for a build that has not happened yet.

Completely undoable project. No vinyl floors with electric heating. If you want warm floors in a whole house, you need hydronic. And no plastic flooring. Spending almost 20K just to have warm floors buys a lot of fuzzy slippers.