Personally I haven't seen that many kdramas with tragic endings. Most of the sad endings are more hopeful and less tragic (like in Scarlet heart). So I'm kinda optimistic about this one.
Initially I thought that after the king fell in love with the queen and every thing was all sunshine and rainbows, the chef and the actual Queen's soul will switch again and Bong Hwan will wake up and find out that the history changed a little about King Cheoljong as well as his own reality (because he took down Chief Han's family in the past) and is now clear of all charges. This hypothesis went down the drain after episode 13 where the Queen's soul was seen floating in the river with the implication being that she didn't swap with the chef and instead actually died (because of which Bong hwan is in a coma coz his body doesn't have a soul).
Which brought me to my second hypothesis i.e. a Scarlet heart ending. You know when IU's character dies in the past she returns to herself in the present. So I thought that the king and the queen will get together and be happy and live a full life and when the queen dies later, her/his soul will return back to the present. The only problem with this theory is that when the queen fell into a vegetative state and the chef returned to his own body in the future, it was shown that the amount of time he spent in the queen's body, the same amount of time he's been in the coma. So if the chef's character has to wake up and live his life then the queen will have to die early which means a tragic ending atleast for the king and the queen of the past. I'm guessing this is what will happen and that chef Bong hwan will meet the king's reincarnation in the present and either become friends or be involved with him (he can also have a romantic storyline with any of the other female character's reincarnations). I'll personally vote for a bl ending.