In the U.S., you can get flour, even white flour, with whatever you want in it. However, the most common additions to flour in the U.S. are a vitamin package, iron, enzymes, potassium bromate, and ascorbic acid (Vitamin C). There are also bleaching agents used to bleach some flours but they are not usually identified by chemical name in the list of flour ingredients. However, the flour will usually be indicated as being bleached in the ingredients list and in the spec sheets as well.
The vitamin package is essentially composed of B vitamins, which are added to replace B vitamins lost during milling. In 1997, folic acid, which is also a B vitamin, was added to most vitamin packages when it was discovered that folic acid can prevent infant neural tube defects. It is also considered a heart healthy vitamin. The enzyme additive is usually diastatic barley malt (malted barley flour) but there are also fungal and bacterial forms. The active enzymes are amylase enzymes that work on damaged starch in the flour to release the natural sugars from the flour. U.S. flours are considerably more prone to starch damage, which usually occurs during milling but which can also be higher if grains are damaged (e.g., sprout damage). Consequently, there is more damaged starch for the amylase enzymes to work on. European flours usually have less damaged starch than U.S. flours. Since enzymes are usually not added to European flours, there is usually less sugar released from the damaged starch in those flours, and it can take a while for the enzymes naturally present in the flour to do their work.
Vitamin C is added to some flours because it acts as an oxidizing agent (by virtue of acting with atmospheric oxygen), which makes it easier to form the gluten network (by preventing the gluten bonds from breaking down) during kneading of the dough. An example of a flour with ascorbic acid added is GM's Superlative flour, at http://www.gmiflour.com/gmflour/Flour_SpecSheet/Superlative53521(West).doc
Iron is added to flours to increase its bioavailability, usually for purposes of preventing iron deficiency anemia. The potassium bromate is added to flour (usually certain higher protein flours) for a variety of purposes, which have been discussed on several occasions elsewhere on this forum.
In general, organic flours tend to have the fewest additives, as can be seen for the General Mills Sperry Organic HyGluten flour at http://www.gmiflour.com/gmflour/Flour_SpecSheet/OrganicHighGluten57881(Both).doc
As might be expected, apart from protein/gluten considerations, most of the additives to flours are not likely to be implicated in the kneading process. However, I believe that bromates and Vitamin C in flours are likely to have an effect on the machine kneading process, particularly the potassium bromate.