A Cessna 172 pilot reported taking evasive action to avoid a skydive aircraft viewed on TIS-B broadcast resulted in a NMAC.

Narrative

During a flight to complete my instrument currency; my safety pilot and I completed a landing at ZZZ to a full stop using Runway XX. After taxing back to Runway XX we declared our intention to turn left crosswind and depart to the East. About the time we took off from RWY XX the King Air had dropped its parajumpers and declared their intention of entering the downwind on a 45 angle of entry. Another Cessna skyhawk also declared their intentions to enter the downwind on a 45 but moments later declared that they would make a right 360 to make spacing for the King air entering the downwind. At this time we could see both tracks on the TIS-B broadcast and we had visual of the other skyhawk conducting a right 360. About abeam the numbers for Runway XX in the left downwind our plane indicated a traffic advisory of a plane 200 feet above and behind to our right. At that moment I pulled the throttle to idle and pitched the plane into a descending left turn. I called out on CTAF that we diving in the downwind to avoid traffic. The King Air then declared turning left base for the runway. We were still getting traffic advisory so I banked harder left to a turn towards the north and made a radio call that the King Air was descending on us. The King air then called turning final and that we were no factor. At this point I could see them on final and began climbing back out and returning to a easterly heading.