Can I use nylon-made paint tray to contain paints?
Nylon is a type of plastic.
Most cheap painting brushes are made of nylon. They can withstand the solvents used in the oil painting process.
Since nylon is a family of compounds with different properties, and the paint tray you mention is marketed as such, you can be sure its resistance, durability, and breathability are all within the characteristics of what one can expect from it. It should be as easy to clean as any other plastic tray.