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k1  =>
        vname1 => [ v1, t1, f1 ] # note: I changed the () to []
...

k3  =>
        vname3 => [ v3, t3, f3 ]

# Assign an array (ref) to the HoH value $hash{$key}{$valname}
   $hash{$key}{$valname}   = [ $value, $type, $flag ]; # option 1
@{ $hash{$key}{$valname} } = ( $value, $type, $flag ); # option 2

my $type  = ${ $hash{$key}{$valname} }[1]; # individual value
my @array = @{ $hash{$key}{$valname} };    # all values

foreach my $key ( keys %hash )
{
...
        print join( "\t", @{ $hash{$key}{$valname} } ), "\n";
    }
}

use Data::Dumper;
print Dumper( \%hash );