I want to record script using amf proxy server but in http sampler setting amf type is missing. How should i enable amf type in amf proxy server.
Apache JMeter does not propose AMF Sampler due to License incompatibility of BlazeDS with Apache licence.
Regarding your login issue you should check that you add a CookieManager to your test plan. Then check you add the Java beans used by your Flex Application to send objects to Flex layer.
You can have a look at:
https://www.ubik-ingenierie.com/blog/load-testing-flex-with-jmeter-made-easy/
https://www.ubik-ingenierie.com/blog/ubikloadpack-flex-amf-plugin-4-0-for-apache-jmeter-released/
Performance testing Flex applications