Floor then wainscot. There will be trim at bottom of the wainscot that should go over the floor and cover the gap between the floor and wall.

I'd also suggest painting or finishing the wainscot before you put it up and then touch-up as necessary.

Remove flooring and wallpaper first. The sheetrock may need a lot of work/replacement, depending on the wall paper.

Paint walls, install wainscoting, install flooring, install trim.

Reasoning as follows:

Sloppy work first---repairing walls and painting. With the flooring removed, messes are less problem.

Once the walls are done, install the wainscoting. Again, no flooring means no scarring finished flooring. And no dirt/dust in the grooves of new flooring. To determine the height of the finished floor---so the wainscoting can be properly installed, snap a chalk line on the wall or make a floor height template. And install the top trim or chair railing now. Painting the wainscoting now would be good, no dripping/etc. on new flooring.

Install flooring. With the wainscoting already installed, there is a better reference for the necessary gap around the flooring perimeter required for floating flooring.

Only thing left is the base/shoe molding. Paint before installing and touch up as necessary.

Sloppy work first---repairing walls and painting. With the flooring removed, messes are less problem.

Agreed with wood flooring. When building from scratch, I put ceramic and stone first; they're tougher and properly covered are less prone to damage.

Even with the flooring last, be prepared to touch-up the walls later.

How'd your project go? I'm searching the exact title of your post from last year....what did you do first & now that you already did it, any suggestions on the order of this, thanks!