I'm wondering whether there will be a problem during luggage check-in (carry on) if I carry multiple bottles (max 3 bottles each 100mL) of Tea Tree oil.
According to the Australian Tee Tree industry website:
Why is tea tree oil classified as a dangerous good?
It has flammable properties, with a FLASH POINT (closed cup) under 60.5°C. According to the IATA DGR liquids having flash point less or equal to 60.5°C are classified as dangerous goods (Class 3).
How may dangerous goods be transported by air?
They are not permitted in passengers' or crews' baggage.
Therefore the answer is no, you may not carry tea tree oil in your carry-on or check-in luggage, as it is a highly flammable liquid.
Websites selling tea tree oil confirm it as well:
NOTE: This low-flashpoint oil (136°F) will ship Ground Only, regardless of the shipping method you choose at checkout. It cannot ship outside the lower 48 U.S. states or USPS.
You will have absolutely no problem with carrying tree tea oil in your checking luggage. If you can have the receipts of the product with you that would be great if in case the customs has any questions, which I doubt. Just make sure you pack it properly (Leak proof).