You probaby haven't gotten any comments because your peace lily is not a lily at all. Spathiphyllum are aroids....a completely different sort of plant :-)

If the soil is consistently moist and has flies (really fungus gnats) that means it is overly water retentive or you are watering too often. A very common occurrence with most bagged potting soils. And this can lead to root rots as well as creating a very favorable environment for the gnats. I'd look for or create a faster draining soil mix - check out the 5-1-1 recipes on the Container Gardening forum.

And I really dislike any self watering containers. They were developed for the gardener's convenience rather than the health of the plant and can often lead to these overwatering issues, especially with an inferior soil mix.

And check out the Houseplanst forum if you have further questions. Spaths are most often discussed there.