I dont' think I'd dare flush WBCL, whatever they say, esp if in a flat. I live in a ground floor flat and frequently get backflow in my loo and shower due to blockages from the upstairs flats. Last year my flat was flooded with sewage water to the point where I had to move out and get new carpets for the entire flat. I just wouldn't want to risk doing that to anyone, tbh.
I don't take the litter straight out to the bin. I put it in nappy sacks and dump it in the bathroom, then take it out when I go out. I also have a litter locker which isn't great, but does help a bit (when I use it) as you can seal away the soiled litter until you empty it. I still use the nappy sacks (you are supposed to be able to put the litter straight into the litter locker but that's a bit risky as you can get to the end of the bag suddenly and find it all falls out!
) then put that in the litter locker. It's basically just a thick plastic bag but you turn the handle to tie it and put the lid down. It's just a fancy bucket really, but it's useful for storing soiled litter if it's not easy to take it straight out to the bin. I find it still smells a bit when you open it, but when it's closed there was no smell. It might be useful for you.