There are a bunch of CF-PCMCIA adapters like the one AmigaKit sells. They work fantastic, and using the CF and FAT filesystem drivers on Amiga means you can use DOS/Windohs formatted flash cards to transfer easily.
Linux does support Amiga filesystem which I use pretty often for backing up Amiga hard drives (and now Flash IDE disks). I can't tell you much about Windohs since I switched my PC to Linux from MS-DOS 6 & Windohs 3.1 haha. WinUAE exists and is popular, and I think supports AFFS.
An A1200 compatible PCMCIA ethernet card costs $20-30 and will let you transfer over your LAN or the internet, which is another option.