I have been watering my flower field from the lagoon for a long time now how long does it take for flowers to appear?

It takes a lot of water - be patient.

Thank you

Putting more people on the job will make it go faster, but then again you may not be able to afford taking villagers from their jobs. (Though mine are rarely on the job anyway :P )

I just completed this puzzle but it still shows just green grass and no flowers. Should flowers have appeared there?

What does your puzzle screen show?

The puzzle screen shows that it's completed and shows the picture of all the flowers there but they didn't actually appear in the green patch.

The absence of the flower graphic won't affect your ability to complete the game, since the puzzle completion has been registered on the puzzle screen. If you drop a villager in that field, what reaction do they have? How many player slots do you have going? If you have other game slots active, do the other slots have that puzzle solved?

It says that they "feel very well in the garden". I just have the one game going right now.

That's very odd. We haven't seen that kind of thing happen before with only a single game going. Have you quit the game and launched it again to see if that corrects the problem?