While not a bad solution (I gave it an upvote), here's a couple of points to consider:

• You've added two blank lines between the __DATA1__ and __DATA2__ blocks. As a result, you've needed the "$#file1 - 1" calculation.
• I think using splice here is overkill: a simple array slice would suffice.

Putting those two points into effect:

#!/usr/bin/env perl

use strict;
use warnings;

use Inline::Files;

my @file1 = <DATA1>;
my @file2 = <DATA2>;

print for @file2[@file1 .. $#file2];

__DATA1__
hi
1
hw
r 
u
hi
2
hw
r
u
__DATA2__
hi
1
hw
r
u
hi
2
hw
r
u
hi
3
hw
r
u
[download]

Output:

hi
3
hw
r
u
[download]