The IDs you have are not Gene IDs (which is what NCBI is calling Entrez Gene IDs these days), but are instead GeneInfo Identifiers, which are a different beast altogether. However, it appears that KEGGREST will use the GI numbers. You just have to use keggConv(). And fortunately for us, there is an example of how to do this in the help page for keggConv():
Examples:
head(keggConv("eco", "ncbi-geneid")) ## conversion from NCBI GeneID to
## KEGG ID for E. coli genes
head(keggConv("ncbi-geneid", "eco")) ## opposite direction
head(keggConv("ncbi-gi", c("hsa:10458", "ece:Z5100"))) ## conversion from KEGG ID
## to NCBI GI
## conversion from NCBI GI to KEGG ID when the organism code is not known:
head(keggConv("genes", "ncbi-geneid:3113320"))
And evidently you can do more than one species:
> keggConv("genes", c("ncbi-gi:222080100", "ncbi-gi:15804211"))
ncbi-gi:222080100 ncbi-gi:15804211
"hsa:10458" "ece:Z5100"
So it looks like a two step process. Convert your GI numbers to KEGG IDs, and then do the lookup using keggGet(). You will then have to use e.g. lapply() to get out the exact data you want, but that is just a base R problem
.