Hi,
mysql (or any other traditional SQL database for that matter) is not an ideal storage for logs, their performance range is usually much lower to what a log infrastructure can collect.
Assuming mysql is the botlleneck in your installation, you can tell syslog-ng to slow down incoming logs to the pace of mysql using the flags(flow-control) in your log {} statement, however that will mean that everything will slow down to what mysql can give you.
In any other case, you will need to improve mysql performance (larger box, better disks, tuning parameters etc).
Or you start using something else for logs, ElasticSearch is much better suited for this use-case. Splunk is better, but is quite expensive. One Identity (formerly Balabit) has SSB that can cope with a lot of logs and can be a good step forward, but that's proprietary too.
Cheers,
Bazsi