So - I just survived an outbreak of Kitten Rot with only one dwarven casualty. It's been one full season since my last outbreak, so I'm pretty certain I'm in the clear. Anyway, I wanted to share my observations of and techniques for dealing with FB syndrome outbreaks, in the hope that it could help someone else.
1.) The smaller a creature is, the easier it is to infect. Your cats and dogs will be doomed, as well as most larger livestock like donkeys or cows. Large creatures like bears and elephants might be safe - or, more accurately, they won't start getting sick until your dwarves are already dying en masse, so you'll have bigger fish to fry by then.
2.) This may be common sense, but multiple contacts with contaminants increase the likelihood of infection. Dwarves with many infected pets are more likely to get sick than those with only one, dwarves hanging out in miasma-filled areas are more likely to get infected than those in areas with only occasional clouds, etc.
3.) Syndromes vary wildly from Beast to Beast. Your mileage can (and will) vary quite a bit.
HOW IT SPREADS (known):
1.) Fighting the FB - venom/poison can infect the injured, secretions can infect any who touch them, breath and dust can infect anyone nearby.
2.) FB Extract/Blood - Walking through FB extract or blood can infect dwarves or animals. While this is known to be worst for FB's with dust attacks (since they leave extract everywhere), please note that outbreaks can (and will) occur from other attack types as well.
HOW IT COULD SPREAD (theorized, from most likely to least likely):
1.) FB Miasma - My fort was doing just fine (except for the one injured dwarf who was bitten) until the corpse of a venomous FB began rotting right in the middle of all my workshops. Soon after, several animals caught The Rot.
2.) Miasma from the infected - Those spending a lot of time near the infected are most at risk, although this could be based on simple proximity rather than the miasma itself.
3.) Blood from the infected - Possible but unknown. Areas with blood from the infected often have miasma, so this could just be a repeat of the above.
4.) Invisible dustings of contaminants - Some have theorized that amounts of extract or blood smaller than a dusting or spattering could be tracked invisibly by DF, and still be enough to infect. My situation provided no evidence of this, but different syndromes are different.
1.) Create ponds with ramps in meeting areas and/or high-traffic hallways, filling them to a depth of 2-4 before un-designating them. Dwarves and animals will walk through them, washing off contaminants. The water will get pretty vile, so make sure this is not designated as a water source. Once they start to get full of contaminants, loo(k)ing at the water may cause a crash.
2.) Have multiple Butcher Shops at the ready.
3.) Have many built, empty coffins prepared for burial (include pets) at all times.
4.) Have a well-stocked hospital with many beds and accessible soap/water.
5.) Prepare a pet disposal area - a single-tile hallway that ends with a lever, a non-pet-passable door, and a spike trap connected to said lever can help eliminate non-butcherable infected pets.
FIGHTING THE ROT:
1.) Get rid of the Forgotten Beast corpse and all parts to prevent as many miasma infections as possible.
2.) Set all tiles with Forgotten Beast blood and extract as Restricted-Traffic designations, so dwarves will path around them. Consider building walls around it to prevent animals from walking through, or wait for idle dwarves to clean them.
3.) Have idle dwarves available for cleaning and burial. These are low-priority actions, so you may need to disable labors for some dwarves.
4.) Keep an eye on the Health screen within Z-Status. Any animals requiring Diagnosis are infected, and any dwarves likely are as well. Note that the Diagnosis requirement will not pop up when infected, but when they start showing symptoms, so many animals are likely already doomed even if they do not show a need for health care. Check constantly to be sure.
5.) Immediately butcher or otherwise eliminate all infected animals ASAP. Do the same with all dogs and cats. Either butcher or closely monitor all larger creatures, particularly cows, donkeys, camels, jaguars, and other mid-size animals. If an infected animal is in an unneeded room alone, lock the doors and wait it out. Its worth noting that my only surviving animal is a single war bear - all cows, bulls, and donkeys were infected.
6.) Save and load constantly. A normally-minor glitch prevents badly infected creatures from dying until the fortress is loaded anew, and dead infectees are much less dangerous than live, wandering ones who spread miasma throughout the fortress. You may see instances where you load your fort to see a dozen animals die within minutes and get immediately stuffed into miasma-preventing tombs. This is also notable because dead animals somehow produce less miasma than infected ones.
7.) Disable all non-medical labors on at least a couple of dwarves, to ensure that infected dwarves are treated ASAP.
I hope this helps. I would encourage you to be careful, as different syndromes are different, so your experience will likely be very different than my own. That said, I was able to survive with only one casualty (not including the 30 animals), so hopefully this advice will help you out as well.