I've been feeding bees with a half gallon fruit juice jar on the lid for many years. It is completely easy to monitor (I can see if they need feed from my back door!), easy to replace with more feed (rarely even wear a veil to put on a new jar), avoids tempting robbers like the entrance feeders do, you don't keep drowning your bees like the inside feeders do, and the apparatus is essentially free.
I make my own tops out of plywood so that I can use a feeder hole. However, this method might not work with the top of a Flow hive.
There is a hole the size of the jar's cap in the hive top that the jar rests in. You have small holes in the jar cap for the bees to drink the syrup from. You tip the jar, cap down, into the hole and it rests there very securely. It doesn't drip because of the suction inside the jar. The bees have to actively suck on the syrup for it to release.
In fact, my bees are going through about half a jar a day. I have
to replace the empty half gallon jar every two days. The picture shows
an empty jar that I'm about to replace with a full one. I think you'll
find this by far the easiest and most efficient way to feed them syrup.