What should be the range of rank in the KVPY to secure admission in IISER?

It’s not possible to answer this definitively as IISERs don’t make information regarding cut-off public. But entry to IISER through KVPY is easier compared to other gateways like the IISER Aptitude Test. 

One of my friends was selected for KVPY SX in 2017. At the time of college choices, his options were Pune, Kolkata, TVM, Tirupati. He finally got IISER Kolkata. 

According to him, if you get a KVPY fellowship, there is a good chance that you will get into an IISER. But going by the trends of the last few years, you will need a rank below 600, in order to get IISER Pune.