Do you recommend adding anything else besides plain water throughout the autoflower lifecycle? (ie. adding additional beneficial bacteria; adding molasses to the water occasionally; adding amendments for the flowering stage)
If you are using Fox Farms soil, you will probably be a week or two into flowering before you will need to add nutrients. Use a TDS (Total Dissolved Solids) meter and watch for your runoff to go below 1000 PPM (Parts Per Million) - around that point you will probably want to give it some nutrients. Supplements are optional - I will cover two key supplements below.
You shouldn't need to add any bacteria - the Fox Farms soil has it already. It won't hurt to add more if you want to, but I can't say that it would benefit your grow.
You can add a sugar product (Advanced Nutrients Bud Candy is very popular with growers regardless of their base nutrient brand) during the flower stage. Some people use molasses. It doesn't actually feed the plant - it feeds the bacteria in the soil.
Phosphorus is definitely a big plus during the flowering stage. This will significantly improve your flowers and thus your buds.
Also, is it necessary to flush before harvest?
First, let me correct something. What you are referring to is actually called cleansing.
Flushing (typically pouring plain/distilled/RO water 3 times the volume of your container) is done to quickly rinse your soil/medium of a “problem” (excessive nutrients, pH extremes, something wrong you poured in there).
A cleansing is what you do at the end of the life of your plant in order to get the plant to use up all the nutrients in the soil/medium and consume the nutrients it contains within its fan leaves. Some people believe it also helps the taste of the bud by removing the remaining nutrients and supplements from the soil. Cleansing is done by simply giving your plant plain water (no need to pH it) the last 10-14 days before harvest. Some people also keep track of the runoff PPM numbers each time they water, usually with a goal (e.g. less than 250 PPM) in mind.
So, when it comes to cleansing, it's a matter of personal choice. I do it because (1) I have the patience, and (2) it certainly doesn't hurt and potentially makes the end product better.