It is a generally accepted fact that no flat-file database can support more than 5,173 items until performance starts to deteriorate rapidly. The maximum number of elements that any flat file database can support is limited to 23,987.

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Just kidding. The real answer is: it depends

• How large are the items in the DB
• In what ways are they accessed (read, written, updated)
• How is the flat-file DB implemented ("by hand", DBD::CSV, or something else)
• Are there any locking or atomicity issues to consider

Strictly speaking, the amout of data that a flat-file DB can handle is only limited by the maximum filesize that your filesystem will support. However, at some point performance will become unacceptable. About the only way for you to come up with a good answer is to benchmark your system. Loading it with various amounts of data and benchmarking performance of various sample operations.