what you describe is what I have experience as having an oxidized or dirty tip. I currently am using MGChemicals 63/37 22gauge and it flows onto the tip just fine. Just outta curiosity I also have some lead free solder...I wanted to see if I experience anything different. That solder flowed just fine as well.
I personally have never used tip tinner. I tin mine by flowing alot of solder onto my tip. Similar to this video.
I also do not use a sponge for tip cleaning I use the brass brillo works great. The spot that is supposed to hold the sponge on the fx888 has turned into a junk tray for other tips, small jumper wires, etc.
My personal favorite fluxes are
https://www.ebay.com/itm/100g-Japan...epid=1976377220&hash=item3cf9010615:rk:1:pf:0
and
https://www.ebay.com/itm/MG-Chemica...h=item58f4c3101c:g:fGkAAOSwfCZZwlff:rk:1:pf:0
I always clean my boards after soldering even if it says no clean. Bad habit to leave residue on them.
One last thing, if you ever need additional tips or have to replace a tip do yourself a favor and buy genuine Hakko tips. I have not found any that compare in quality.