Again, may not be an issue at all for loads of applications. But I used a lot of "flat file databases" in the past, and found it's not an issue right up to the point that it is. Overall, I found SQLite simple, fast, and ubiquitous enough to serve as a good fopen() replacement. In some cases it can even be faster!
Are you sure? I thought it could be if the first write had more data than the size of the kernel/fs-driver buffer, not all of it would be written, and then it could be interrupted when another thread calls write() with a small buffer that gets written in one go.
You maybe thinking of stdio buffering, where calls to printf etc get split into multiple write calls. Then in those cases, it's possible to get errant interleaved writes.