The Flores Bike rides directory is way too vast to list here. Here are however some general guidelines, and advice.
Bring a Nelles or Periplus map. Then choose your bike carefully, especially if you want to go for several days. I would recommend a semi automatic bike, like a "bebek" or those with gears/clutches like a Yamaha or Honda.
Enduro bikes are hard to find on Flores, but you can rent one from Bali or Lombok.
Now is possible to rent in Labuanbajo the CRF 150 or KLX150 between 250/300 k per day.