Dragon Gem Locations and Guide
There are four different Dragon Gems hidden throughout the world which will grant you the powers to summon a powerful Dragon form on Ryu and Fou-Lu. If you've played Breath of Fire 3 they work kind of similarly to how Dragon Genes were in that game. The Dragon Gems on this page shouldn't be confused with the 6 Dragons you can speak to and ask for help. They grant you abilities whereas the Dragon Gems grant you different Dragon Forms.
Below I have a guide for each Dragon Gem, how to reach it and where to find it. The first Dragon Gem you come across is on Mt Giga which is about midway through the game. Also if you missed one of these Dragon Gems you can simply go back for it, the world map can be confusing but there's no location you can't go back to in the game.
Wyvern - Mt Giga
The Fire Dragon Gem which grants the Wyvern/Weyr Dragon Forms is found on Mt. Giga which is to the south of Shikk. It's really hard to miss if you're running through the Mt. Giga area, the Dragon Gem is right out in the open and pretty easy to get to.
Behemoth - ? Area on N. Islands
You can find the Earth Dragon Gem which grants the Behemoth/Mammoth Dragon Forms in the second portion of the Sand Flats area in N. Islands. On the map you'll find a "?" location between the towns of Pabpab and Saldine, which is where you will want to enter to find the Dragon Gem (use my map above).
In order to make it through the area you'll basically have to run right by this Dragon Gem, if you are for some reason having trouble finding it then I recommend you isolate your search to the one area of the map where you find a lot of grass. Towards the end of the Salt Flats area (heading south) you'll find a raised platform with a lot of grass and trees. This is where the Dragon Gem is.
Mutant - En Jhou Ruins
In order to gain access to the En Jhou Ruins you'll need to speak with the man that's wandering around Koshka, it's a really small town north of Chiqua. This dungeon is an optional part of the game which becomes available when you make it to Chiqua and speak with the Chinese man about gaining entry to the capital.
The Mutant Dragon Gene is at the very bottom of the En Jhou Ruins. In order to even get into the dungeon though, you'll need to put Ershin in your party and bust down the fake wall in the room on the first floor. Once you do this, the rest of the dungeon is pretty darn straight forward.
Take the ladder down into the bottom of the temple where the roots are then take the slides down and make you way over to the eastern side of the room. There's a doorway over here which will lead you into another much darker room which is where you'll find the Mutant Dragon Gene. If my directions are confusing don't worry, it's pretty straight forward once you're here.
Myrmidon - ? Spot near Fou-Lu's Tomb
The Myrmidon/Knight Dragon Gem is found in the same fields you went through with Fou-Lu earlier in the game, right next to his tomb. While running through this area you'll come across a large open area with scorched earth, the Myrmidon Dragon Gem is found on an off shoot of this area, obscured fairly well by the bushes.
If you're having trouble finding it search the bushes around the edge of the area with scorched earth for a path, alternating camera angles when necessary.