Multithread fastq processing with kseq.h in C++11?
You might take a look at my FQFeeder library (https://github.com/rob-p/FQFeeder), which pairs the kseq parser with a multi-producer / multi-consumer queue to allow efficient parallel processing of the parsed reads.  The library contains an example program to demonstrate how to use it with multiple threads.  It's worth noting that kseq is already very fast, so multi-threading only really makes sense if worker threads are doing non-trivial work on each read so that you can then make the parsing and processing concurrent (have the processing keep pace with kseq).

I'll note that my library relies on a header-only MPMC implementation and so technically isn't "only using the standard library", but you're already relying on kseq.h, so omitting third-party libraries must not be a hard constraint.