How can aviatrix do the integration with multiple cloud vendors smoothly without much downtime to applications?

The short answer is that yes it is a smooth process.

Did you take the ACE Associate certification yet? We are covering this question there in detail. Also, take a look here for more details and videos.

https://youtube.com/netJoints

For example

https://www.youtube.com/watch?v=6lR4Eyac68U