Air India is part of Star Alliance, but you're coming from a small airport with little to no international flights to a destination with few international flights and no. You're looking at at least a couple of stops along the way. MCI-ORD on United, then ORD-HYD on Air India with a connection in Delhi or Mumbai or somewhere. Or through Air Canada.

OneWorld is a better option because British Airways flies non-stop to HYD from Heathrow, as does Cathay Pacific and Qatar. You can make easy 2-hop connections from Kansas City with those choices. With Star, your options are pretty limited and you'll have to fly Air India at some point.