It would sound more natural if you say, "We are playing basketball together."

It is not natural. "We are playing basketball together," is correct and natural as Jazz noted. Adverbs of frequency usually go before the verb, but can go in other positions for stylistic reasons. - I often drink coffee, but I never drink tea. Other adverbs usually go after any direct or indirect objects but before any prepositional phrases of place or time. - He speaks Russian well. - We play basketball together at the gym on Fridays. There is a recent tendency to put some adverbs of manner before the verb. - He repairs cars carefully. => He carefully repairs cars.

If you want it to sound native, then just drop "together." It doesn't have to go anywhere in the sentence. So: "We are playing basketball." The "together" is implied. If you want it to sound like everyday speech, then you would use a contraction: "We're playing basketball." Hope this helps. Good luck!