I have flown often with oil paints and because of my fear of confiscation have always put them in my checked baggage and had no problem.
I always pack them carefully (wrapped in absorbent paper towels, in a closed plastic container), along with a printout of the following page from Air Canada and MSDS forms, following these instructions (look under PAINT and see the heading "Exceptions" for how to pack artist's colors):
When I traveled to Paris I even printed out and attached a statement in French, stating that I was a painter and my materials were not flammable and officially permitted.
When I travel to the U.S.A. (I am Canadian), I also put a printout of the TSA site page stating they are allowed:
However, I really wish I could just use a carry-on bag so I don't have to worry about my suitcase going AWOL. And, unfortunately, these days it costs extra to check a bag.
I had always interpreted the TSA instructions to apply to checked items and not carry-on, but on re-reading the information just now, it seems okay to carry on the paints as long as the tubes are small (make sure you exclude that giant tube of Titanium White, even if it is almost empty) and you can prove they are not flammable. I think I will try this next time, and bring a printout from TSA along with the MSDS which proves that the items are non-flammable.
Of course, you can't bring a huge array of colors and you have to limit your toiletries since everything has to fit into that teeny ziploc bag, AND if you need a largish painting support you are out of luck.
MSDS forms are available online from Gamblin. Look under Gamblin Oil Painting Materials, Artist Grade Oils, and then click on the individual pigment:
MSDS forms are also available from Winsor & Newton, which provides for individual colors as well as their paint in general:
Some of my less mainstream brands such as Michael Harding have not responded to requests for MSDS. I figure if I can prove that oil paints for artist's in general are not flammable, they will probaby accept that none of them are likely to be dangerous.
It is also a good idea, if you check the paints, to politely request in writing that they replace everything in the same manner it was found. I have heard horror stories of people opening their suitcase to find everything coated in cadmium red after an officer failed to put the cap back on a tube correctly. That's enough to ruin your day for sure!