I don't always fly to teach workshops, but when I do this is how I pack.
I take two suitcases - one for clothes and the other for all the art supplies: All the liquids, tubes of gels, acrylic paint and all the sharp things like scissors and box cutters go in this suitcase. Your art supply suitcase is checked luggage - never carry on!
Mindful of the current 50 lb weight limit per suitcase, I don't overpack or bring more than I will use for painting. I precut my watercolor paper to fit the suitcase (16x20 approx) - and it stays flat. But the real concern in packing are the liquids and paints.
Oh, those pesky leaks! We have all experienced leaking jar lids and paint caps that weren't screwed down tight. First, make certain lids and caps are tight. Then, for added protection, wrap and secure all lids with one inch white artist tape. It's time consuming, but worth it!
Next, double bag all paint and liquids in one gallon re-sealable plastic bags. It's a bit cautious and over-engineered, but everything arrives intact. As added protection, I put bubble wrap around each bag of paint.
Sharp things, brushes, hand barrier cream, strong box tape, drawing pencils etc. all go in another plastic bag.
One more important step... Write WATER-BASED ART SUPPLIES on all plastic bags.
Thirty-three weeks a year traveling all over this planet, I have never been questioned, searched or stopped by TSA. I have also never had a mishap with leaking paints. So when asked "What's in the suitcase?" - you answer "Water-based art supplies." Then, zip it! Say no more and keep smiling!
Paint always goes in your checked luggage! Keep smiling!