If you are referring to the claim that; at some time prior to the 1967 Constitutional Referendum, which amended the Australian Constitution to allow the Commonwealth of Australia to make laws effecting Australian aborigines; there was any law which classed aboriginal people with "flora and fauna" or not human then the claim is false. Also the claim which is sometimes circulated that it was possible to obtain a license under the "Flora and Fauna Act" to shoot aborigines is also false.

The earliest version of the claim that can be identified is from 1970 and it often resurfaces as a political trope when discussing "how bad it was for aborigines in the old days".

Prior to 1967 laws specifically concerning aborigines were restricted to the various Australian States. Most had some form of an "Aboriginal Protection Act" all of which were quite similar and tended to restrict who could be identified as aboriginal for receipt of benefits and occupancy of aboriginal reserves, to restrict sale of alcohol to aborigines, to appoint and empower a Chief Protector of Aborigines etc. The Acts varied in whether they gave aborigines the right to vote or not. Queensland and Western Australia did not give the vote. No Australian State or Territory ever classified aborigines under a "Flora and Fauna Act"

See this link to a 20 March 2018 Australian Broadcasting Commission "Fact Check" discussing when and how the myth entered the public and political sphere. https://www.abc.net.au/news/2018-03-20/fact-check-flora-and-fauna-1967-referendum/9550650