if I build on a floodplain I thought that this made my city prone to disease
Technically, disease probability is based on the tiles in the FatX, rather than the city-tile itself.
So your Floodplain-town is only subject to disease if there are
other Floodplain (or Marsh) tiles in the vicinity. There usually are, of course (as in your screenie above), but at least in theory it should be possible for the map generator to place a 'sole' Desert tile next to a river (= Floodplain), which happens to be surrounded by non-disease-causing tiles (e.g. Deserts, Plains, Hills, Mountains). Same applies with Jungle: founding a city automatically clears the Jungle (to Grassland, which has no disease risk), but the city will usually still have Jungle in the FatX, which can continue to cause disease until it's all cleared as well.
You shouldn't let the
possibility of disease put you off founding a city on Floodplains, though. Floodplain towns tend to be food-rich (especially after irrigation, and especially after leaving Despotism), and (re)grow quickly, so population losses are usually easily replaced. Jungle-towns are a trickier prospect in the short-term, since they tend to be food-poor and slow-growing until you've spent a lot of Worker-turns slash-n-burning. Once you have Workers (or Slaves) to burn, you may want to consider using Colonies to insta-clear (and road) Jungle Lux- and/or StratRes-tiles before sending in a Settler to plant a city, but this is not really feasible in the early game.
However, acquiring Sanitation (not sure if you also have to build Hospitals—I'd have to check the .biq) removes all risk of terrain-caused disease.