Where does the "Frog's Theme" appear in Chrono Trigger?
Solution 1:
A simple way to hear any character's theme (assuming that they have joined your group yet) is to not have them in the party, talk to them at The End of Time and tell them you want to change your party, except when you're at the point where their sidequests are available. Regardless of whether you actually change your party or not, that character's theme will begin playing.
I recommend playing the entire game when you can as it is great but, for your purposes, it would be easiest to use one of the latter game saves, head to the end of time (remove Frog from the party if he's with you) and talk to Frog, telling him you want him in the party. Frog permanently joins the group when you hand him the Masamune and from then, except for brief points when you're in inescapable dungeons, you can pretty much go to The End of Time at your leisure either via time gates or using the epoch.
In the first list, the most convenient would be save state #14 slot 2 as the epoch is right nearby and you have completed Frog's quest.
Note that this is the regular version of the song as is played throughout the entirety of the game. The version found in the OST and the linked youtube video does not appear to be in the game. I checked every narrative scene that featured Frog during the game and every ending and all of them that played Frog's Theme played the same looped/abbreviated version, not the one featured in the OST. I even checked the Playstation and DS remakes and neither version featured the OST version, not even in their music box sound test sort of deal. They all play the abbreviated version covered in the OST version in the youtube video from 0:16-0:46 and then loop.
If you're looking to separate out the voices in the full version featured in the OST (meaning the first 16 seconds), I'm afraid you're going to need to brush up on your listening skills or seek out further resources. I'm not sure if it will be helpful, but I came across a musical score for this version of the song here, but I'm not sure of the tempo/time signature as the midi version they link doesn't fit the exact same timing although the melody sounds correct as near as I can tell.
Solution 2:
Frog's Theme shows up the first time you meet Frog, near the beginning of the game. Following the first link you posted, if you use game save #1, slot #2, you should be right at the point where you meet Frog. My memory is a bit hazy, so it may be slightly before or after that-- once you've loaded the state, check to make sure Frog isn't already with you; if so, load an earlier one.
That being said, you can just search his theme on Youtube and find it no problem. Any particular reason you need to find it in the game?