It's not 100% safe but many risk it anyway. I know providers who claim they caught something through DATY. You are exchanging bodily fluids

I would have to say DATY holds the danger of hormonally castrating a guy by ingestion of her vaginal secretions.

I would separate the risks into 2 categories: HIV and other STDs.  The risk for contracting HIV via cunnilingus is extremely low, and even the CDC is not sure that there is a single documented case (these things are always difficult to track, because the people in the studies usually engage in multiple high risk behaviors).  It is a theoretical risk.  The theoretical risk is higher if the woman is having her period (because blood transmits HIV), and likewise higher if you have a cut or sore or something on or in your mouth that would expose your blood vessels to infection.  So flossing your teeth right before you go down on a woman, in theory, increases this theoretical risk.  But it is an extremely small risk in any event.

The other STDs, however, present a different problem.  I would be particularly concerned about herpes, because it is incurable.  If you are infected with the herpes virus, you will be infected for the rest of your life.  It's not life threatening, of course, but it's pretty gross to think you will be carrying around an STD for as long as you live.

A woman can be infected (and, theoretically, contagious) with herpes even if there is no open sore.  But certainly going down on a woman who appears to have a sore or infection around her vagina is crazy (and vice versa; a woman would be taking an insane risk to perform oral sex on a guy who had a sore on his penis).  It strikes me as always a good idea to perform sex with strangers in a well lit environment, where you can see what you are getting into.  Dental dam or not, I would never risk going down on a woman with open sores.

Nothing is ever risk free, even with a barrier.  But of the various activities a man and a woman can engage in, oral sex on the woman is the safest (apart from masturbation) -- certainly safer than vaginal sex, anal sex and fellatio.