Why not spend a few $$ on a larger flash drive? 8gb drives cost less than $10 these days.
1gb is the recommended bare minimum for a non-GUI base install of Debian. Running a Linux system with only the absolute bare minimum hardware is never fun.
Or just install Puppy (100mb), SliTaz (35mb), or Tinycore (8mb) and then you'll have lots of space on your 1gb.