The REST service is also available from the KEGGREST R / Bioconductor package.

library(KEGGREST)
keggLink("pathway", "hsa:10327")  # pathways gene 10327 is in
p = keggLink("hsa", "pathway")
map = split(names(p), unname(p))  # gene -> pathway map

Queries follow closely the API provided by KEGG.

I don't believe that KEGG is accessible through BioMart. However, you can use the TogoWS REST service to retrieve that information. Look at the examples in the KEGG GENES section on that page.

I know it's an old question but wanted to update that kegg_enzyme was added to the list of attributes in bioMart, it will return the pathway (the number portion of mapXXXXX pathway) and the enzyme EC number.

try(ensembl <-
            biomaRt::useMart("ensembl", dataset = "mmusculus_gene_ensembl"))
    try(annot <-
          biomaRt::getBM(
            c(
              "ensembl_gene_id",
              "mgi_symbol",
              "chromosome_name",
              "strand",
              "start_position",
              "end_position",
              "gene_biotype",
              "kegg_enzyme"
            ),
            mart = ensembl
          ))

Will return (for instance):

ensembl_gene_id mgi_symbol chromosome_name strand start_position end_position   gene_biotype               kegg_enzyme

1048 ENSMUSG00000030409       Dmpk               7      1       19083849     19093821 protein_coding            04714+2.7.11.1
1049 ENSMUSG00000030409       Dmpk               7      1       19083849     19093821 protein_coding            05165+2.7.11.1
1050 ENSMUSG00000030409       Dmpk               7      1       19083849     19093821 protein_coding            04150+2.7.11.1
1051 ENSMUSG00000030409       Dmpk               7      1       19083849     19093821 protein_coding            04151+2.7.11.1
1052 ENSMUSG00000030409       Dmpk               7      1       19083849     19093821 protein_coding            05170+2.7.11.1
1053 ENSMUSG00000030409       Dmpk               7      1       19083849     19093821 protein_coding            04926+2.7.11.1
1054 ENSMUSG00000030409       Dmpk               7      1       19083849     19093821 protein_coding            05163+2.7.11.1

You can use 'graphite' R-package.