I also have an iPhone 6 and a slightly different Panasonic model KX-TGEA20. The paring initially worked without any problem, but I had to disconnect the paring recently for a reason I cannot even recall. When I tried to pair the phones again I kept receiving an 'unsuccessful paring' error message. After spending two hours on the phone with the folks at Panasonic they suggested I send the phones back to them for replacement. As a last ditch effort I remembered an old, but often useful procedure. I disconnect the power from the base station, waited a minute, plugged it back in and it worked the first time I tried to pair the phone again. Don't know why the Panasonic techs did not think of this.
Hope this helps you or anyone looking for an answer to the pairing problem they may be experiencing. It seems to be a common problem.