
In everyday Australian workplace English, “I’m flat out” commonly means “I’m extremely busy” or “I’m working as hard as I can”. It does not mean that the speaker is lying down. The central idea of flat out is operating at the maximum speed or intensity.
A: Can you help today?
B: I’m flat out till three.
It is stronger than “I’m busy”. “I have many works” is not a natural alternative, because work is usually uncountable in this sense; say “I have a lot of work”. Flat out can also describe a machine operating at full speed.
https://dictionary.cambridge.org/dictionary/english/flat-out
https://www.abc.net.au/news/2009-09-17/im-stuffed-migrants-boggled-by-aussie-slang/1433256
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