It is Muttar to talk to a cousin (unless you are in a family where you Mamash don’t know your cousing like you would a stranger).
The Mechaber very conspicuously leaves talking out of the list of Assur interactions with Arayos. Hence, talking is not inherently Derech Chibah (while other flirtatious actions are).
R’ Moshe says that in today’s society, if a guy is going to be friends with a girl while there are so many guys available to be friends with, there is an inherent psychological assumption that the reason he wants to have some form of relationship is because, well, she’s a girl. That, he says, makes even talking inherently Derech Chibah and Assur Min Hatorah.
By one’s cousins, this assumption doesn’t seem to apply, and certainly if the cousins grow up together. Thus, in this case, just talking (in a non-inappropriate way, obviously) should not be Assur.