Simple way to get the shape needed is to use thin cardboard or thick brown paper.
Cut the various pieces and sellotape together to gee an accurate template. Remember to allow for the awkward bit under fires, fridge doors etc
Measure twice and cut once
While still on the van floor, mark one side TOP....
Get your flooring...2m wide stuff should be enough and whatever length you need (measure widest and longest sections of floor).
Place the flooring face up and then the template on top. If flooring is patterned align as accurate as you can...nothing worse than a squinty floor.
Tape template to flooring. Mark around the template with a pen, but allow 2 or 3 inches on all sides if possible to allow for the odd areas such as under a fire or fridge door etc.
Try you cut out section for size. It should be a bit larger than fits neatly. Do any basic corner cuts at this stage to allow the edges to overlap
If all is well, scrub floor with a cloth and thinners and allow to dry.
Get some carpet fitter spray glue and starting at one end, spray some glue on the floor...just about a couple of feet to start with...and lay the first couple of feet of flooring. Once you have it lined up correctly, peel back slightly and spray some more, then lay...then spray, then lay and so on.
I use an aquaroll to hold down the flooring at the start after I have laid the first couple of feet...filled of course.
Once the main floor has been laid, then turn to the edges. If you can get them under the furniture and fittings, fine. If not, careful trimming will be required. I find one of those wallpaper cutting wheels is good for marking / cutting the top coat of vinyl and then a Stanley knife to cut through backing.depends of thickness of flooring as to whether it will cut right through.
A bit more spray glue at the edges and a roll with a wallpaper joint wheel and you're done.
Any edges that can't be fitted under trim or furniture can be sealed with a thin bead of silicone.clear or a colour to match interior of van.
I have used the above method on several vans and in various house bathrooms over the years.
Patience is the key.