The distance to Velankani from Chennai would be around 315 kms. You can take either ECR or GST road till Pondy. ECR road is scenic compared to the GST. Tindivanam to Pondy is fantastic empty stretch.
From there its Cuddalore-Chidambaram-Sirgali-Karalikal-Nagore-Nagapatinam-Velankani. Roads are in good condition, but most of it are single laned. Expect the travel time between 5-8 hrs (depending on the start time & stoppages)
Edit: Where do you plan to stay in Velankani?
Seagate resorts/Clinton Inn are good....I would avoid the MGM cottages (Rooms are good, but expensive)