Optimal database structure for fast inserts
The problem with MySQL's InnoDB engine is that the storage architecture is essentially using index-organized tables, which will unfortunately experience performance issues for large numbers of inserts when the target table is large.  The only case in which this can be mitigated is if you have sequential inserts, that is, the primary key of the set of inserts follows a sequence.

For high ingestion rates of data, different technologies are recommended, such as Cassandra which uses a log-structured merge tree, or in your case, I might recommend TokuDB, which has been acquired by Percona, and which uses a technology called a fractal tree index, which is essentially creative way to cache, pre-sort, and batch insert into your index-organized table (of course, there's much more to it than that, but no need to go into the details here.)

Long story short, if you have moderately high ingestion rates, you need a heap organized table structure implemented by databases like Oracle and PostgreSQL, and if you have very high ingestion rates, you need to use a database like Cassandra or TokuDB.