fruit flies/fungus gnats!
I'd like to believe that I am Zen enough to handle these annoying little winged ones, but after finding 3 flies in your tea a person is bound to get somewhat annoyed, so it's time to go fly trapping.
Many of these flies I surmise are actually fungus gnats rather than fruit flies because I always have this problem in the fall/winter when the plants come in and they are harder for me to control compared to the fruit flies that make their home in my compost pail. As the links show, you can distinguish the two readily by their squished abdomens (unless you have pretty good eyesight when they're buzzing around or can catch them when one's actually settled down). The gnats have a darker slightly pointed end abdomen and the fruit flies' are lighter and rounded.
The issue with the fungus gnat is that it is somewhat difficult to control because they lay their eggs in the soil that is damp and unless you keep only desert plants they seem to be quite happy in general houseplant conditions. So I find elimination difficult and for me, the best I can do is simply control them.
Though the flying adult gnats are a pain, it's really the larvae that are the biggest issue as they feed on plant roots and can weaken them though generally won't kill a plant outright, who wants buggy weakened plants?
If you see the gnats hanging around and want to see if any of your plants have larvae, you can water the plant very well until you get a little pooling on top. If you see tiny swimming whitish-clear things floating about, you've probably got gnat larvae and will need to treat and prevent.
Some general methods to keep the fungus gnats from taking over:
(1) Allow soil to dry out between watering. I hate having to water each individual plant at different times, but as they all have different needs in terms of watering and are of different sizes/pot boundedness (terrible I know, saving up for more pots!), it's important to water them only as needed. This will also keep down the general issue of overwatering/root rot most people have.
(2) Prevent the adult gnats from laying their eggs in general by covering the soil layer will small pebbles (my method), or sand (someone swears by their plants on this). Others say that a sprinkling of diatomaceous earth is a good preventative as the larvae will be injured and die from the sharp material, but as it is expensive and people and pets can potentially be harmed breathing it in I don't use it. The pebbles and sand will make it very difficult for the adults to find openings to the soil to lay their eggs as well make it difficult for the larvae to eggs easily as adults. I've heard that the sand can potentially injure and kill soil emerging adults too like diatomaceous earth.
(3) Neem oil/water drenches seem to make a bit of a difference in killing the larvae/eggs. The only issue is making sure you can cover the entire area well to get to all the crevices eggs or larvae might be hiding.
(4) Avoid soil mixes with woody bits or wood mulches in your household plants (hard to do and even I am unable to do this entirely). These mixes/mulches can harbor the gnat eggs from the start. As many of my plants were outside much of the year, they probably picked it up there and despite my prior treatments before bringing the plants indoors, you can imagine gnats probably breed faster than bunnies even with only a few around.
(5) You can trap the larvae like slugs with potato pieces and discard the pieces as they become infested with larvae. It's not a complete cure but it makes a dent in the adult fly populations.
(6) As with many bugs, the colors yellow and red are attractive and if you use vaseline/petroleum jelly, smear a good amount of the greasy stuff on something red or yellow you aren't a huge fan and wait for flies to get stuck on it. Then wipe/rinse and repeat! I don't use vaseline and the like, so maybe honey might do?
(7) You can also build a trap using a small mouth container (beer bottles or cans usually for me) filled with part way some sort of sweet liquid such as beer or red wine (the red color and sugar is helpful), juice, sugar/yeast or a combination of those and and make a paper funnel on top to attract and capture the flies/gnats.
(Tunnel of Death for the gnats/flies!)
(Kirkland beer, pretty good, gnat/flies approve too)
A shallow dish of the stuff works too but I don't know if these gnats are Houdinis and easily escape from those or fall in and drown easily, though I've been very successful capturing flies/gnats this way too:
Just a note to check up on these containers every so often because they are a great place for mold to grow (very beautiful looking blue-green mold I'd like to add) and to make sure that it's not in a location a pet can get to. My dog found a can of it one day after it became a home to mold too and she had a puke-fest for a day thereafter. Joy.