I'm going to comment on various timestamps throughout the video, and explain what I personally may have done in the given situation instead. You do not have to take my advice if you don't want to, but these timestamps stood out to me in particular:
0:02 - Not entirely sure why you jumped over your crown here. In my opinion, it's important to stay as grounded as you can when you throw the crown, as the crown is extremely good against King K. Rool. Since Chrom was in shield as a reaction to the crown coming back, that might have been a good opportunity to go for a grab. With that said, the two nairs you did after the crown toss was a fine option.
0:15 - Good jab, but I think a grab would have worked here against Chrom's dancing blade. I love using up throw at early percents to rack up a nasty 20% early on.
0:44 - Right around here, Chrom sent you upwards in a position that horizontally has you near the ledge. This may have been a good chance to try out the Blunderbuss vacuum to stage spike Chrom, if he did not suspect it.
1:14 - Same situation as 0:15, good jab but a back or down throw may have been a better option.
1:30 - I liked the edgeguard attempt, but your best move in this situation may have been back air. King K. Rool's arm has some priority, and with the right spacing, it could prevent Chrom from coming back. Alternatively, it may have been better to stay on stage and punish Chrom's ledge get up option, as allowing him to return to the stage before you do gives Chrom an advantage in neutral.
1:36 - Not sure why the crown toss was used here. Since Chrom used a dash attack here, this may have been a good opportunity to either grab or forward tilt.
2:21 - Same as 0:15 and 1:14. I think up throw would have been the most optimal here to rack up damage.
3:02 - Like 0:44, this may have been a good opportunity to try the blunderbuss vacuum to stage spike Chrom.
3:13 - Just wanted to point out how good of a forward tilt this was. Great spacing, and it's one of King K. Rool's more reliable kill options at higher percents. I noticed the move was not used to much throughout the video, but this is one of the reasons why I think it's one of the kremling king's most important moves.
3:32 - Same advice as 0:15, 1:14, and 2:21.
3:57 - As a follow up to 0:02, you successfully grabbed Chrom after he put up his shield from the crown toss. I just wanted to put out how good of an option this was, as it's taking advantage of the fact that Chrom is under pressure. I also liked the down throw and up tilt immediately afterwards, as even though it didn't kill him, it put him in a disadvantageous position off-stage. With that said, the up tilt sent him too high upwards for an off-stage punish, so staying on the left platform and punishing his return with a forward air or counter may have been better.
4:23 - The down smash here seemed really unsafe. It was a bit laggy, so the Chrom had some time to retreat and throw the crown again. I think a grab would have landed here since you shielded his forward air before you used down smash, and with Chrom at 126%, there is a good chance that back throw would have killed Chrom here.
4:32 - Like in 4:23, this would have been a good opportunity for a back throw kill to end the match. It's good to keep in mind the rock-paper-scissors dynamic of Smash, where attacks beat grabs, grabs beat shields, and shields beat attacks. Chrom's dash attack is laggy, so if you ever shield it, a grab afterwards is a good punish option.
4:38 - Good down throw. Since Chrom was over 130%, it may have been good to try a downwards angled forward smash or forward tilt. Forward smash would have killed if it connected. However, some opponents are able to mash out even around 130% to 150%, so make sure that the followup punish is swift.
4:45 - The decisive ending of the match. It looked like Chrom was hoping to get back on solid ground for the final kill, so maybe punishing his landing here off of the platform may have been the best option. It's a pretty tricky situation all around though, but you played well.
Overall thoughts: You definitely are aware of King K. Rool's moveset and some of his best tools. With that said, you seem to jump over your crown and lose it quite a bit. I also did not notice some of his moves being used too often, like up tilt and forward tilt. Up tilt has a great disjoint above King K. Rool that cans serve as an anti-air option, and forward tilt has traits like armor, good range, and kill power. I also feel like the blunderbuss was not used too often either, and the vacuum was not used once throughout the match. The canon serves as a slower, farther reaching projectile option, and I feel like Chrom would not appreciate dealing with it if it reaches him off-stage. The vacuum could also serve to get him off-stage for kills or kill setups.
King K. Rool also does not mind staying back a bit and pressure from afar with his crown and blunderbuss, and characters like Chrom and Ganondorf need to get up close to do anything. If you are playing as King K. Rool and currently winning neutral, sometimes staying away from Chrom and maintaining the neutral position would be good. Forward tilt can also block Chrom's attacks if you feel like the Chrom is being overly aggressive. Lastly, in my opinion, going off-stage against Chrom should be done if you feel like you can meteor him with the vacuum or back-air. Otherwise, it's better to stay on stage in order to make sure that Chrom is unable to be in an advantageous state upon returning. Otherwise, missing an off-stage edgeguard punish allows Chrom is safely return, and then it makes it hard for you to get back to the stage safely.
Good stuff overall, but I hope my tips could help you out. You are definitely capable of getting back into Elite with the kremling king, and as long as you keep in mind all of your options, you can come out on top. I would love to try some King K. Rool dittos sometime too if you would want to play against mine. Please keep up the good work, it's great to see more people using the kroc!