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Are you interested in knowing if H3AuCl4O is allowed to be carried on American Airlines, or any airline? Internationally, or within a specific country?
In the USA, the Federal Aviation Administration might have applicable regulations, but the Transportation Security Administration has other regulations that include the carriage of powdered substances on board. (The FAA would determine whether you could have the substance in your checked baggage.)
What is the policy on powders? Are they allowed? link
Starting June 30, 2018, if you are traveling from an international last-point-of-departure to the U.S., powder-based substances in carry-on baggage greater than 350mL or 12 oz. may require additional screening at the central checkpoint. Powder-like substances over 12 oz. or 350mL in carry-on that cannot be resolved at the central checkpoint will not be allowed onto the cabin of the aircraft and will be disposed of.
For your convenience, place powders in your checked bag.
The measures have already been implemented at U.S. airports nationwide to identify and prevent potentially dangerous items from being brought aboard the aircraft. There are no changes to what is allowed in carry-on baggage at U.S. airport checkpoints.
I would suggest contacting the airline directly, or the FAA, to determine whether Gold(III) Chloride Hydrate can be brought aboard or checked in as hold cargo, rather than a public forum mostly dealing with travel, earning and spending points and miles.
In my personal opinion, quantities other than medicinal for personal use would likely not fly with a profile like:
Corrosive to metals, category 1
Skin corrosion, categories 1A,1B,1C
Serious eye damage, category 1
and
Acute toxicity (oral, dermal, inhalation), category 4
Skin irritation, category 2
Eye irritation, category 2
Skin sensitisation, category 1
Specific Target Organ Toxicity – Single exposure, category 3