Since this question is a bit tough, I assume you are already familiar with the Spring Security Kerberos samples that show how to configure kerberos auth with a form auth as fallback.
I have no evidence that it'll work but I think you should be able to chain your kerberos auth with basic auth without any problems. I share my thoughts on this...
Thought 1: FilterChains
The trick to support mulitple authentication methods is to set the order of the authentication filters correctly.
If the order is wrong, the client could hang in the basic auth and might never reach the kerberos authentication filter, because the browser's basic auth dialog would pop up. This might depend a bit on how the basic auth provider and filters are implemented in Spring. Anyway, if the order is correct, the filter next in chain after the kerberos filter (the basic auth filter) will start its work.
Thought 2: Kerberos auth shouldn't break basic auth
The browser should treat the communication with the kerberos service provider different to the communication with the basic auth provider, since the protocols are different.
The SAML communication runs in it's own namespace, thus in my opinion it shouldn't affect the basic auth communication which is based on authorization element in the HTTP header.
EDIT: Even if the assumption about the namespace doesn't play any role in the browsers behavior, step 6 in the sequence diagram will be a crucial point. When the filter chaining is correct, Spring should return a 401 response like 401 - Access denied - WWW-authenticate - Basic realm = "your domain"
which will force your browser into basic auth.
Thought 3: Spnego Negotiate in Spring Security Kerberos
The Spnego configuration in the Spring Security Kerberos documentation is acutally build upon those thoughts. This can be seen in the samples, too, in line 49 and 50 of this WebSecurityConfig.java
I would be surprised if you experience troubles.
One last thought
If no requirements force you to do a basic auth, I would recommend to not use it. Better stay with a token based authentication. Even if I don't fully agree on all details of this blog it explains why basic auth shouldn't be used, if you can avoid it.