I configured kibana with a server.basePath: "/kibana" in the config file. That worked fine before installing the x-pack plugin.
After installing xpack, I got stuck in a redirect loop. See the logs for the details.
When I remove the server.basePath statement in the config, I can login (without the reversed proxy).
{"type":"response","@timestamp":"2017-03-08T19:19:13Z","tags":[],"pid":76697,"method":"get","statusCode":302,"req":{"url":"/","method":"get","headers":{"accept":"text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,/;q=0.8","accept-language":"nl-NL,nl;q=0.8,en-US;q=0.6,en;q=0.4","x-cnection":"close","host":"kibana","iv-user":"xxx","user-agent":"Mozilla/5.0 (Windows NT 6.1; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/56.0.2924.87 Safari/537.36","via":"HTTP/1.1 nl020isam018.ad.intra:443","upgrade-insecure-requests":"1","iv_server_name":"xxx","x-forwarded-for":"10.40.13.20"},"remoteAddress":"10.74.81.107","userAgent":"10.74.81.107"},"res":{"statusCode":302,"responseTime":8,"contentLength":9},"message":"GET / 302 8ms - 9.0B"}
{"type":"response","@timestamp":"2017-03-08T19:19:13Z","tags":[],"pid":76697,"method":"get","statusCode":302,"req":{"url":"/kibana/login?next=%2F","method":"get","headers":{"accept":"text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,/;q=0.8","accept-language":"nl-NL,nl;q=0.8,en-US;q=0.6,en;q=0.4","x-cnection":"close","host":"kibana","iv-user":"xxx","user-agent":"Mozilla/5.0 (Windows NT 6.1; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/56.0.2924.87 Safari/537.36","via":"HTTP/1.1 nl020isam018.ad.intra:443","upgrade-insecure-requests":"1","iv_server_name":"xxx","x-forwarded-for":"10.40.13.20"},"remoteAddress":"10.74.81.107","userAgent":"10.74.81.107"},"res":{"statusCode":302,"responseTime":4,"contentLength":9},"message":"GET /kibana/login?next=%2F 302 4ms - 9.0B"}
{"type":"response","@timestamp":"2017-03-08T19:19:13Z","tags":[],"pid":76697,"method":"get","statusCode":302,"req":{"url":"/kibana/login?next=%2Fkibana%2Flogin%3Fnext%3D%252F","method":"get","headers":{"accept":"text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,/;q=0.8","accept-language":"nl-NL,nl;q=0.8,en-US;q=0.6,en;q=0.4","x-cnection":"close","host":"kibana","iv-user":"xxx","user-agent":"Mozilla/5.0 (Windows NT 6.1; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/56.0.2924.87 Safari/537.36","via":"HTTP/1.1 nl020isam018.ad.intra:443","upgrade-insecure-requests":"1","iv_server_name":"xxx","x-forwarded-for":"10.40.13.20"},"remoteAddress":"10.74.81.107","userAgent":"10.74.81.107"},"res":{"statusCode":302,"responseTime":3,"contentLength":9},"message":"GET /kibana/login?next=%2Fkibana%2Flogin%3Fnext%3D%252F 302 3ms - 9.0B"}
{"type":"response","@timestamp":"2017-03-08T19:19:13Z","tags":[],"pid":76697,"method":"get","statusCode":302,"req":{"url":"/kibana/login?next=%2Fkibana%2Flogin%3Fnext%3D%252Fkibana%252Flogin%253Fnext%253D%25252F","method":"get","headers":{"accept":"text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,/;q=0.8","accept-language":"nl-NL,nl;q=0.8,en-US;q=0.6,en;q=0.4","x-cnection":"close","host":"kibana","iv-user":"xxx","user-agent":"Mozilla/5.0 (Windows NT 6.1; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/56.0.2924.87 Safari/537.36","via":"HTTP/1.1 nl020isam018.ad.intra:443","upgrade-insecure-requests":"1","iv_server_name":"xxx","x-forwarded-for":"10.40.13.20"},"remoteAddress":"10.74.81.107","userAgent":"10.74.81.107"},"res":{"statusCode":302,"responseTime":3,"contentLength":9},"message":"GET /kibana/login?next=%2Fkibana%2Flogin%3Fnext%3D%252Fkibana%252Flogin%253Fnext%253D%25252F 302 3ms - 9.0B"}
{"type":"response","@timestamp":"2017-03-08T19:19:13Z","tags":[],"pid":76697,"method":"get","statusCode":302,"req":{"url":"/kibana/login?next=%2Fkibana%2Flogin%3Fnext%3D%252Fkibana%252Flogin%253Fnext%253D%25252Fkibana%25252Flogin%25253Fnext%25253D%2525252F","method":"get","headers":{"accept":"text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,/;q=0.8","accept-language":"nl-NL,nl;q=0.8,en-US;q=0.6,en;q=0.4","x-cnection":"close","host":"kibana","iv-user":"xxx","user-agent":"Mozilla/5.0 (Windows NT 6.1; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/56.0.2924.87 Safari/537.36","via":"HTTP/1.1 nl020isam018.ad.intra:443","upgrade-insecure-requests":"1","iv_server_name":"xxx","x-forwarded-for":"10.40.13.20"},"remoteAddress":"10.74.81.107","userAgent":"10.74.81.107"},"res":{"statusCode":302,"responseTime":2,"contentLength":9},"message":"GET /kibana/login?next=%2Fkibana%2Flogin%3Fnext%3D%252Fkibana%252Flogin%253Fnext%253D%25252Fkibana%25252Flogin%25253Fnext%25253D%2525252F 302 2ms - 9.0B"}