As given, your example does not match anything. If you use re 'debug'; you will get a fairly cryptic trace of what the regular expression is doing:

$ perl -Mre=debug -E 'my @m='lkjkljkjlkhkjkfjkfkvklkv'=~/^\w*(kl(?1)\w*).*?(kv)/g; say for @m;'
Compiling REx "^\w*(kl(?1)\w*).*?(kv)"
Final program:
   1: SBOL /^/ (2)
   2: STAR (4)
   3:   POSIXU\w (0)
   4: OPEN1 (6)
   6:   EXACT <kl> (8)
   8:   GOSUB1-4:4 (11)
  11:   STAR (13)
  12:     POSIXU\w (0)
  13: CLOSE1 (15)
  15: MINMOD (16)
  16: STAR (18)
  17:   REG_ANY (0)
  18: OPEN2 (20)
  20:   EXACT <kv> (22)
  22: CLOSE2 (24)
  24: END (0)
floating "klkl" at 0..9223372036854775807 (checking floating) anchored(SBOL) minlen 6 
Matching REx "^\w*(kl(?1)\w*).*?(kv)" against "lkjkljkjlkhkjkfjkfkvklkv"
Intuit: trying to determine minimum start position...
  doing 'check' fbm scan, 0..22 gave -1
  Did not find floating substr "klkl"...
Match rejected by optimizer
Freeing REx: "^\w*(kl(?1)\w*).*?(kv)"

The trace says your match never got started because the string being matched does not contain 'klkl'. The first 'kl' is the literal one from your regular expression; the second is because of the recursion. I believe that even if the string contained 'klkl' there would be no match, because there is no way for the recursion to end; it would just look for 'klklkl', then 'klklklkl', and so on.

Can you say what you expect @m to contain in your example?

And can you provide an example where you match against the shortest possible string that you want to match successfully?

There are no "recursive" inner matches returned.

It's unclear what you want but the following demonstrates how to match only at the top level of a recursive match.

  DB<173> x 'bla[[abc]]foo' =~ / ( \[ (?1)* \w* \] ) /xg;
0  '[[abc]]'
[download]

Not what you wanted?

Then see how (not) to ask a question

  DB<150> x @m='lkjkljkjlkhkjkfjkfkvklkv'=~/^\w*(kl(?1)\w*).*?(kv)/g;
  empty array
[download]

?

SSCCE?