Do your flats have drainage holes and are you bottom-watering, BWhite?
My technique for watering flats is to set the flat (with holes) in a basin that contains a couple inches of water. The soil can soak there for about 30 minutes, then the flat is lifted out of the basin and allowed to drain.
Sometimes, I use flats with no holes under that "holey" flat. I am cautious, however, that all excess water has dripped away before I double up the flats like that.
A single, initial soaking is usually sufficient for the time that it takes for whatever seeds to germinate. Often, that "single soaking" is over several hours. Starter mixes are often very dry coming out to the bag but all excess water is allowed to drain away.
Make everything as simple as possible but not simpler. ~ Albert Einstein