Perhaps a two-stage split rather than a regex?

$ perl -Mstrict -Mwarnings -E '
my $str = q{Klhl21 NM_001033352 chr4 + 152008890 152017677 152008942 1
+52015628 4 152008890,152012299,152014306,152015334, 152009963,1520127
+05,152014379,152017677,};
say for map { split m{,} } split m{\s+}, $str;'
Klhl21
NM_001033352
chr4
+
152008890
152017677
152008942
152015628
4
152008890
152012299
152014306
152015334
152009963
152012705
152014379
152017677
$
[download]

I hope this is helpful.