[NFC][clang] Fix static analyzer concerns

HeaderIncludesCallback and HeaderIncludesJSONCallback classes may own
resources and free them in the destructor. However they don't have copy
user-written constructors/assignment operators, so an attempt to copy a
HeaderIncludesCallback object will use compiler-generated copy
constructor which will only do dummy copy and afterwards there will be
use-after-free issues.

Reviewed By: aaron.ballman, tahonermann

Differential Revision: https://reviews.llvm.org/D155842