In practice, would this sentence work better as, "I'll give you an example"? Though technically, that's the future tense, it's what English speakers say immediately before giving an example.
This sentence would be said while in the process of giving an example :)
Nope :) The accusative is for specific direct objects (I am giving the example, for example). And there is no indirect object/recipient of the example (I am giving you an example). No need for either. :)
Is there a dıfference between saying: Sadece bir örnek veriyorum and Bir örnek sadece veriyorum? Which one means I am only giving an example?
Yes...the second one is grammatically incorrect. :) The first one is fine.