Fun with flags!

Python 2, Score = 68 89

This solution uses the hash of the flag image file to create an index into a list of the country abbreviations. If more than one flag hashed to an index, only the first abbreviation will be returned (so it will fail some of those tests with more than one country in a hash bucket). This algorithm does however guarantee one correct answer for every non-empty hash bucket.

i=hash(open('f.png').read())%99*2
print'kgmviruasefridusvakpsmbtgrpwcdsdauninrsyalsg--game--espyscmtyebhgqom--kh--inhudjbw--ltroilbicv--jonaugke--svhtbg--simcknbnpelcplgncmmacimytnttlytgcflirsvemhtzuyqaerbfbepa--uzaenearcl--jmbbphkzrwieet'[i:i+2]

This program is 247 characters.

A more readable version:

encoded = 'kgmviruasefridusvakpsmbtgrpwcdsdauninrsyalsg--game--espyscmtyebhgqom--kh--inhudjbw--ltroilbicv--jonaugke--svhtbg--simcknbnpelcplgncmmacimytnttlytgcflirsvemhtzuyqaerbfbepa--uzaenearcl--jmbbphkzrwieet'
index = hash(open('f.png').read())%99 * 2
print encoded[index : index+2]

Building the encoded string

To build the encoded string, I use a function to read in the flag files as strings, generate a hash from the string, and reduce the hash to a limited number of hash buckets:

def encode(buckets):
    lookup = {}
    for fn in os.listdir('flags'):
        name = fn[:2]
        signature = hash(open('flags/'+fn).read()) % buckets
        lookup[signature] = lookup.get(signature, '')+name
    return lookup

to return a dictionary of countries that match each signature, then use some code to convert the dictionary into a lookup string:

encoded = ''.join(lookup.get(v, '--')[:2] for v in range(buckets))

I needed to experiment a bit with which values of buckets gives the best results.

CJam, 139 141

There's a lot of unprintables in the code, so here's the xxd hexdump:

00000000: 7132 3925 3162 226d cec5 9635 b14b 69ee  q29%1b"m...5.Ki.
00000010: d9d0 66e8 97b8 e88d 2366 7857 9595 1c73  ..f.....#fxW...s
00000020: 9324 11b2 ddb8 7a3f 19ed bd37 07c0 cb86  .$....z?...7....
00000030: 394e b34a ecf0 8c9b f300 a216 2e2e 594a  9N.J..........YJ
00000040: 9a6b 3b2f 250a 9a25 783b 0e49 3e9c 6ab9  .k;/%..%x;.I>.j.
00000050: 8d6d d729 42d0 85f3 657b 7d86 af48 c6cb  .m.)B...e{}..H..
00000060: f7ff 980f b81c dd5e e8cb 4e34 d8ec edca  .......^..N4....
00000070: 6646 1b4d 7605 8937 ed58 2302 1cc1 ebfd  fF.Mv..7.X#.....
00000080: 16d3 b53e 3e2c d879 fe33 feef dd65 d49f  ...>>,.y.3...e..
00000090: 5d73 7ced 92e6 9526 c186 00bf d2a8 ffaa  ]s|....&........
000000a0: 65a0 3001 f42a 94d7 592f ebe7 8bdf 97a7  e.0..*..Y/......
000000b0: 0681 8ee1 9e0e 424b f6a1 4c50 1c8a 8de5  ......BK..LP....
000000c0: 481a 388c 6eaa 0c43 e1db 69df 567b 323f  H.8.n..C..i.V{2?
000000d0: 2573 c4ce b348 6fff 37e0 55b4 7c9a 7e7d  %s...Ho.7.U.|.~}
000000e0: 73a4 ef74 2b99 b765 2a2d d99f 986a 355c  s..t+..e*-...j5\
000000f0: db22 3236 3362 3236 6227 6166 2b32 2f3d  ."263b26b'af+2/=

This is exactly 256 bytes, with the program doing:

q29%                          Read input and keep every 29th char
    1b                        Sum code points
      "..."                   Push long string
           263b               Convert long string to base 263
               26b            Convert result to base 26
                  'af+        Add 'a to each element in the resulting array
                      2/      Split into chunks of length 2
                        =     Index sum cyclically to extract output

Run the program with the command

java -Dfile.encoding=ISO-8859-1 -jar cjam-0.6.5.jar flags.cjam < f.png

Thanks to @Dennis for help with getting this submission working.