Living were you do, teak or mohagony should be good choices as would rosewood such as Cocobolo. Any Local wood that can be fashioned into tools can also be used for Knitting Needles. Flex is not so much an issue as tight grain and strength.
Getting a true straight grained piece to work from is essential, careful tapering of the working ends with sufficient pointyness is particular important if you work with different types of wool some will almost require a long very tapered end, the butt end can be finished with a knob or bead I have sets of older needles that were made both ways and good smooth finish and TaDa you have knitting needles.
I have a couple of sets of Japanese chop sticks that are made from Rosewood and except that there is not butt end to keep the yarn from slipping off they would be perfectly suitable for knitting