Not all klinefelters cases have gynecomastia, so that's not a guarantee. The definitive test would be a karyotype but that's expensive. The cheaper option would be genetic testing like 23andme, but depending on how the aneuploidy developed it might not pick it up. If the extra X is maternal, you wont see it. If the extra X is paternal, you'll see heterozygous base calls in the coding region of the X chromosome. So that's a 50/50 shot of it being invisible on a genetic test.
