You want to get the cumcount and add one. Then use %2 to differentiate between odd or even rows. Then, take the cumulative sum and subtract 1 to start counting from zero.

You can use:

df0['flag'] = ((df0.groupby('KEY').cumcount() + 1) % 2).cumsum() - 1
df0
Out[1]: 
   KEY  flag
0    0      0
1    0      0
2    0      1
3    0      1
4    1      2
5    1      2
6    1      3
7    2      4
8    2      4
9    2      5
10   2      5
11   2      6
12   3      7
13   3      7
14   3      8
15   3      8
16   3      9
17   3      9
18   4     10
19   5     11
20   6     12