TL;DR: Your story will inevitably be compared to Harry Potter purely because of how iconic and influential it is within the "magical school" genre, but I definitely wouldn't say it's too similar.
The story takes place in a fictional country I created.
Harry Potter takes place in England. So that's a big difference right off the bat.
There are 6 main characters, 3 girls and 3 boys.
Harry Potter has three main characters. You're fine there.
They are all "gifted" which are people with special abilities. There are 3 types of gifted, which have names. One can detect when you are lying, one can move objects with their minds, and one can control fire and water.
That's nothing like the Harry Potter magic system. You're fine there.
They go to a day school for gifteds in their country. You start learning and using your powers in the upper school which is 7th-12th grade. Which might be like Hogwarts since it's a school for wizards.
This is probably the thing that will generate the most Harry Potter comparisons. Mind you, "school for people with magical abilities" wasn't the most original concept even before JK Rowling did it. I'd say you'll be fine here as long as your school doesn't have too many obvious similarities to Hogwarts (moving staircases, talking portraits, surrounded by a forest full of centaurs, etc.)
The characters learn about something called the book of destiny which basically the whole plot of this book is them trying to find it. Which is like the Philosophers stone.
I'd say this is actually the complete opposite of Philosopher's Stone. In Philosopher's Stone, they know where the MacGuffin is (in the forbidden third-floor corridor, guarded by Fluffy), but they don't know what it is until the start of the climax. In your story, it sounds like the protagonists know what the MacGuffin is (the Book of Destiny) quite early on, but don't know where it is until the climax. You're fine here... but I await your clarification about what the Book of Destiny actually does.
This isn't final, but I am planning that when they find the book of destiny they go through this room and they have to complete a series of tasks that take them through different rooms until they ultimately end up finding it and destroying it themselves.
Again, this might generate some comparisons to Philosopher's Stone, but again, "having to complete a series of tasks to get to the MacGuffin" is hardly an original concept. As long as the tasks are different to the ones in Philosopher's Stone, you'll be fine.
There is a group of 3 sort of mean girls.
Don't recall anything of the sort in Harry Potter.
There is also a mean boy who might make people think of Draco.
Probably. People are always going to compare your characters to other, vaguely-similar characters. I make a game out of it when I'm watching anime - "hey look, it's [my character] but shorter". Like with your school, as long as your mean boy isn't a blatant Draco rip-off, you should be fine.
They call normal people a name just like the wizards call them muggles.
As long as the word itself isn't "muggle", I see no problem here.
I think your story, by its very nature, is always going to face comparisons to Harry Potter. When you say "young teens attending a magic school", people will think "Harry Potter", because it's just that famous and iconic.
However, it looks like you've already gone into quite a bit of detail in building your world, and particularly, in differentiating it from the Potterverse. You're also aware that people will be looking for similarities, which means you can consciously try and avoid them, to whatever extent you can without detracting from the story. So I think you'll be just fine.
I'll finish my answer by repeating something that Mephistopheles said earlier in the comments, and which you'll see over and over again on this site: if your story is good enough, nobody will care how original it is or not.