I'm pretty sure Natsu will keep the fire dragon king spells. I got the impression that Natsu was only using Igneel's power against Zeref, and not for anyone else. I also got the impression that using Igneel's power doesn't necessarily mean Natsu was using fire dragon king spells. If he was using Igneel's power whenever he used fire dragon king spells, why didn't Happy expressed his surprise when he used them against the Alvarez Army? Why would Natsu hold back against a Spriggan, but not against the War God or fodders? Against Zeref, why did he wait until the final attack to enter fire dragon king mode? The fact that Natsu still had enough power for one more attack against Zeref but was worried it was going to run out kind of goes against the idea that he can store this power and use it bit by bit.
Now, some people have said that he said he was using Igneel's flames when he used demolition fist against Ikusa-Tsunagi, but in the Japanese raws he only mentioned Igneel's name (イグニール ) in the subtext of Fire Dragon King (炎竜王). That's really just there to indicate that when Natsu says "Fire Dragon King" he's referring to Igneel's title. In the actual spoken words, he would have said "炎竜王". When we hear it from the anime, it's likely it will be "en-ryu-ou" as opposed to "Ig-ni-ru". The Imishihui Chinese translations neglect to put Igneel's name altogether. Instead, they just write 火龍王, which is just fire dragon king.
I guess we'll have to see whether or not he can still use the Fire Dragon King spells and how he stacks up against a Spriggan.