You can place up to 27 of 5 different type flowers in the hives to create specialty honey. These honeys are created at a 1 flower to 1 honey ratio with 1 created every hour. Note that it is possible to use the full amount of each type flower on the hives, however, when you collect the honey it comes out in a random order. Due to this reason, it is suggested to stick to one type of flower in any given hive. Right clicking the hive you can choose to "Check flowers stored" to see how many and what type of flower(s) you have in each hive.
In order to collect honey, you will need to use insect repellent on the hive - if you have not done so yet, you can add this item to your toolbelt. You will get a message telling you that you see the bees leaving. Clicking the hive will then give you the option to collect the honey or not. Choosing to not collect it will open the flower deposit interface. Collecting the honey will cause you to begin collecting the special honey and continue to do so until the hive is empty or your inventory is full.
Note that diseased animals and eggs will not consume these items.