What would be the best fluorine containing chemical for this?
Fluorite is the most common one on Earth, I believe. It isn't too unusual, but it is generally found underground rather than in surface deposits.
Would the fluorine containing substance impact the organic bits negatively, and if so, how do I get around this?
Oh, very badly! Hydrofluoric acid is astonishingly nasty stuff. You keep it in containers made from fluorine compounds such as teflon. Anything that's not a fluorine-based compound just isn't oxidised enough, and the HF will eat it.
You might get away with some kind of mucous layer in the stomach and digestive tract, but as it would react with the HF you'd deplete your store of the chemical sooner than you'd like. I'm not sure what kind of organic fluorine-bearing polymer your beasties could use, but you could pick almost anything as they already have clearly pretty weird metabolisms.
I meant breaking the silicates down enough for use, but not necessarily separate it from the oxygen. I read hydrofluoric acid makes the fluoride combine with the silicon, which I do not want.
Oh. In which case don't use HF at all, because you'll lose it.
Just produce some suitable biomineral for claws and teeth and crop or whatever that's just harder than silicates. Something like corundum or carborundum would do. Other questions on this site discuss biosynthesis of superhard minerals. This news article mentions bacteria that can do it. Chomp up the glass and redistribute it like any other nutrient and deposit it appropriately. Job done!
As an alternative, you might consider a basic, rather than acidic digestion using nice hot sodium hydroxide to dissolve quartz and form sodium silicate, commonly known as waterglass. It is a useful compound by itself, but when put in a suitably acidic environment you can precipitate the silica back out again.
This requires some fairly unusal biochemistry and a fairly energetic digestive tract, but TANSTAAFL!
Now you know why plants and marine diatoms make their silica from silicic acid they get from the environment, instead of having to do it the hard way like you want.