Not sure which game you're talking about, since there's a dozen Fire Emblem games and not a single one of them were for the Gameboy Color, but the earlier games were a lot lighter on plot and cutscenes.
The more recent ones have lengthy, forced tutorials full of boring dialogue too, so if it's one of those, just give it some time and it should improve.
If it's the English game that just says "Fire Emblem", that's Fire Emblem 7, which probably has the longest and ploddiest tutorial in the series. It gets better once you're through.
Sacred Stones is Fire Emblem 8. I haven't played it myself, so I don't know how long the tutorial is or how obnoxious the game gets with talking, but Fire Emblem games rarely interrupt the action during the game proper with all that much dialogue. Are you sure you're through the tutorial? Is the dialogue purely plot stuff, or is it an explanation of game features disguised as plot?
I do know that Sacred Stones is considered one of the weakest entries in the series, though.
Bob is right, just press start & no annoying dialouge. Be warned though, sometimes the dialouge hints you to use certain characters to recruit enemy/guest characters.