How risky is it to eat raw flour, as in uncooked dough?
Does eating raw flour or doughs containing raw flour pose a significant food safety risk (i.e., greater than other dry goods or ingredients in your kitchen)?

Yes, as the level of bacteria has not been reduced/killed especially if the dough has been sitting/fermenting and/or contains harmful bacteria.  
Nb: Most flour isn't washed or treated (irradiated) before use.  
Although it is cosidered 'dry' it always contains a level of moisture and it's storage usually allows moisture transfer from the local environment that it is stored/used in.

If so, are there particular cooking or baking processes where we should be most concerned about this risk?

Not really, unless the cooking/baking process does not reach a high enough temperature or a long enough period to reduce/neutralise the bacteria that may be present.

I obviously don't wish to downplay the seriousness of this outbreak. But I am interested in the rationale behind the FDA's warning. In particular, is flour (and raw dough) actually a higher-risk food hazard than any other uncooked ingredient in a kitchen? For example, we all know that raw vegetables and fruits have been responsible for hundreds of outbreaks, but the FDA has not issued a general warning against consumption of raw vegetables and fruit. (Instead, the warnings tend to be against the specific batches of contaminated food, as well as a few specific high-risk raw vegetables like sprouts.)

While it can be argued on the quantities being consumed of flour compared to raw vegetables and fruits, and therefore the level of bacteria that the person is exposed to.  Besides most raw Fruit &amp; Vegetables should be washed, the soil and bacteria can be removed this way, and that is before some of these are peeled/trimmed.  Dried fruit and vegetables after washing (and in some cases peeling), can have a number of processes (such as pre-treated - soaking in an acidic solution, or blanched) and are usually kept in a dry environment.
Minimally processed vegetables (high risk), such as watercress can be irradiated.  FDA article on produce (buying, storing, preparing raw fruit &amp; vegetables)
However, raw nuts still have risks of bacteria (e.g. salmonella).  Most nuts are  treated (pasteurised - steam, blanched, roasted, or fumigated - propylene oxide)

So why has raw flour been singled out for a general prohibition (as opposed to a warning about a specific contaminated batch, which applies to most fruit and vegetable outbreaks, as well as most of the dry goods outbreaks mentioned above)?
Is there some new information that justifies this broad and sweeping FDA prohibition on the basis of a couple outbreaks? (And if contaminated flour is such a big deal now to justify the recall of millions of pounds of flour, what makes this new situation different from most wheat flour, which has been known for decades to have high rates of E. coli and Salmonella contamination, occurring in something like 13% of samples of flour?)

FDA Raw Flour/Dough update
Article on the investigation and the lead to the ban
Any further questions maybe better answered by getting in contact with the FDA
and the academic community.