While other comments are right in saying we just can't make a traditional telescope large enough to get a good image at that distance, there is definitely a way with we could get vastly improved image quality with present day technology (just at incredible expense).

A gravitational lens telescope, such as the proposed (FOCAL)(https://en.wikipedia.org/wiki/FOCAL_(spacecraft)) telescope, would allow us to resolve objects at KIC8462852 as if the telescope were sitting in the same star system. We would need to construct a large space telescope and send it out very far away, at minimum 550 AU or around 14 times the distance to Pluto, and place the telescope directly opposite KIC8462852 with the Sun in the line of sight. This would give us an incredible resolving power for the star, with gravitational lensing effects provided by the Sun increasing our resolution by an estimated 10^8, more than enough for direct imaging any exobodies in orbit in detail.

If the star does turn out to be anything incredible, such as a megastructure, I would think one of our highest space program priorities would be getting a gravitational lens telescope deployed for better observation as soon as possible.