It depends. People who use synthetic fertilizers need to flush occasionally and before harvest to leach salts and excess nutrients from the soil/medium. What kind of soil are you using? It probably has fertilizer in it already if your plants have been growing and not showing any signs of nutrient deficiency. If you're using a common hardware store soil like Sta-Green or Miracle-Gro that advertised something like "feeds for up to 6 months" or anything then yes you will probably want to flush. You do this by watering 3x the volume of the container; a 3 gallon container would take roughly 9 gallons of water to flush adequately.
Honey may contain carbohydrates in the form of simple sugars (primarily glucose and fructose) that could potentially be utilized by the plant and/or soil microbes (if present). Molasses contains more of the complex carbohydrate sucrose (fructose + glucose) as well as fructose and glucose as simple sugars, and it also has a much higher nutrient and mineral content. Molasses contains a significant amount of potassium and some phosphorous as well as calcium, magnesium, iron, copper, manganese and zinc (also selenium of lesser importance). That said, molasses is the better choice for horticultural use and it is also quite available.