BYU Provo has always been my dream school.
GPA: 3.902 UW 4.2 W
ACT: 31 (taking again and hoping for at least a 34)
Extracurriculars:
-Job as a Gymnasics Coach
-Job at a local dry cleaners
-Band
-Former Gymnast
What are my chances to get into BYU based on this?
They aren’t still accepting applications for fall right? I’m assuming you’re applying for winter? Anyway I think you have a really good shot given your high GPA and extracurriculars. Your ACT is fine (the range is about 27-31 so you’re in the top )! Good luck 
Are you LDS? If so, no problem. If not, you’ll need to get recommendations from your church.
You will get in no problem. I got in for fall 2018 with a higher GPA, Slightly lower ACT (Took once with no studying), and a couple less EC. One important thing to realize, you don’t list your EC activities anymore. You right essays on two of them. They care more more about quality and impact than sheer quantity
Just an update: I got accepted for fall 2019!