Those little bottles are exactly what I use. I don't have much issue cleaning flux. What kind of flux are you using?
Maybe I just need a bottle with a smaller tip? I don't know what size tip I have on the two dispensers I have, but it's too large, I think.
Ok, I see why you're having a hard time cleaning, because that's rosin. They call it flux but it's mostly rosin. I use 186 as well when I need rosin.
I use Kester 959T as my main flux, which is no-clean with low solids. It's very liquid but the bottles with the needles control it pretty well and since it's no-clean, it mostly evaporates fairly quickly while working, so adding a lot more than you think you need is generally advantageous.
There's a place for both at my bench. Rosin works better for some things while low-solids flux is better for a lot of other things.
And as far as brushes are concerned, after almost 30 years of soldering, I can't stand them. They tend to gunk up too quickly and since I do mostly SMD work, they tend to brush parts away too easily. Bottles are better, at least for me.
Yeah I have never applied additional flux either. I use Kester 24-6337-0027 and it takes very little clean up compared to most other solders I've used. Just brush the pcbs with alcohol with a tooth brush.
Why/when/where is extra flux needed? When I solder the kits I build I don't seem to have any issues just simply using the rosin-core solder.
It depends. Flux can be used for most normal stuff. Rosin is good for more esoteric work. Rosin can be good for really old and crusty solder joints. It can help flow solder that doesn't want to flow, or it can be used in areas where flux burns off too quickly. I sometimes use them together if I need rosin somewhere that it won't flow and the flux liquifies it so that it gets under parts, etc.
One good example is BGA rework. I use some rosin with flux to get all the pads prepared. The boiling rosin when heating will help the balls settle on their pads quickly. That's just a trick I've figured out over the decades that nobody else might know to try but folks ask me all the time how I get 500+ ball BGAs to solder down reliably using a heat gun.