You need consider to configure your HTTP Outbound Gateway with a HttpComponentsClientHttpRequestFactory. This one is based on the Apache HTTP Client 4.x and its default behavior is a DefaultRedirectStrategy which does a redirect on GET and HEAD methods and when 302, 301 or 307 status is returned for the call.
If you need to redirect POST, consider to configure an underlying HttpClient with a LaxRedirectStrategy.
See more info here: Handling HttpClient Redirects
UPDATE
To configure a LaxRedirectStrategy for the HttpClient used in the HttpComponentsClientHttpRequestFactory you need something like this:
<beans:bean id="httpClientBuilder" class="org.apache.http.impl.client.HttpClients" factory-method="custom">
<beans:property name="redirectStrategy" value="#{new org.apache.http.impl.client.LaxRedirectStrategy()}"/>
</beans:bean>
<beans:bean id="clientHttpRequestFactory"
class="org.springframework.http.client.HttpComponentsClientHttpRequestFactory">
<beans:constructor-arg>
<beans:bean factory-bean="httpClientBuilder" factory-method="build"/>
</beans:constructor-arg>
</beans:bean>
It is kinda pitta to do all that stuff in XML, so consider to move your project to Java & annotation configuration.