EDIT: Crosspost. And thats why she's the Queen
Sorry about my confusing mechanics. I meant all of it related to unhealthiness.
sorry about the Flood Plains. I know it is a flood plains from the start, but the unhealthiness didn't happen for several turns.
It is possible you just didn't realize you had the penalty all along and only recognized it due to hindsight.
I was pop:6 for a long time with no issues. Then all of a sudden I see my city is smoking and it says I have 2 unhealthiness for flood plains when I had no unhealthiness at all except from pop.
This sentence does not make sense because somewhere in it a mechanic is being confused. I am assuming here unhealthiness is substituting for unhappiness. If you see black smoke coming from your city there is also a

face above the city title bar. Yellow 'stink fumes' have a green

face above the city title bar.
If the city is still a population 6 city, then you lost a happiness resource (Black smoke). If it is yellow 'stink fumes' then you either lost a health resource, a jungle grew somewhere, or your borders expanded for the first time and because of that 12 new tiles were taken into acount. If they were floodplains then yes they could be the cause, just as jungle could be the cause.
Going into the city screen you will see

(unhealthiness) <

(health) to the right of the food bar.

(unhappiness) <

(happiness) next to the production bar.
The only thing I did about that time was clear all the forest tiles from the area from rushing troops for fighting.
This is probably the cause if it was yellow stink. As if you had enough floodplains to count as 2

and chopped 4 forests (2

) this could be the culprit. The floodplains just kept doing what they had been doing and as I suspected you just hadn't noticed it. The 2 unhealthiness from the floodplains was there the whole time. But when you lost 1-2 health from chopping forests, you see stink come up and suddenly become interested in tracking your health. That 2

from flood plains wa there before you chopped the forests, you just didn't check it until it was brought to your attention.
Dangit guys floodplains doesn't mean actual floodplains its just his way of saying "unhealthy" so let's move on.
I doubt many if any of us here are blasting away at the misproper use. But now is a good time to explain what to properly call everything by its name so that future threads need not be deciphered.