...you need to crush its head for a quick, humane kill. Flushing it means it will suffocate and drown - NOT very humane. For those on the forum who know me are probably surprised by my response but sometimes it needs to be done. I had an awful experience a couple days ago. I saw a baby chipmunk in the road that had been hit but was still alive - wriggling and probably in pain. I turned around not knowing what I should do - it was not going to make it, that was clear. So I ran it over. I was sick in having to do it (just aimed, closed my eyes and acceclerated) but it was better than leaving it to suffer. We as humans can cause this suffering (mouse-traps, cars, etc.) so I think we need to end the life as quickly as we can.
For future reference have you considered humane release (Have-a-heart)traps? You can get them for a couple dollars at HD, bait it with cheese or peanut butter then drive it a few miles away and release. Some folks say they will return and maybe so but mice are so prolific it almost doesn't matter whether you kill it or just trap and release.
good luck 
lele
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0.1 veiled - Luna
0.2 house geckos - Gaia & Tia (MIA 
0.2 felines - Kyndra and Líta