Interior doors and trim all should be done before the flooring.
Flooring before baseboards.
However when it comes to prefinished flooring i respectfully disagree.
If it is installed with the tile up to the baseboard trim then you should leave about a 1 8 gap that you should fill will caulking.
The baseboards should be primed and painted with one coat.
First remove all obstacles vacuum clean the area before applying the caulk and paint the skirting board mopboard floor molding or base molding.
Caulking the gaps in trim joints and the gap between flooring baseboards improve water impermeability of the floor.
When we do the interior trim and the prefinished bamboo flooring in a house or any prefinished flooring for that matter we always do all the trim first using 3 4 spacers or whatever width the floor you are using is under the doors cased openings and baseboard.
Home owners generally prefer the look of doing the tile first and then installing the baseboard trim.
Spot prime and then add another coat of paint to baseboards because it lessens the chances that something happens to your floors since now you only have to spot prime and add one.
Baseboards are often installed before flooring since they must be finished in place with either stain or paint and this is much easier without worrying about staining the hardwood tile or carpet.
With unfinished hardwood always run the floor first.
Use a utility knife to slice any caulk that secured the baseboard to the wall.