Welcome to Android Central! Moved to the Droid Maxx 2 forum.
If you save an Instagram photo to your phone, I think it goes to the directory called /Pictures/Instagram. Photos there should automatically get added to your Gallery app's database unless there's a file called ".nomedia" in that directory. Use a file manager app to look in the Instagram directory, and if you see a ".nomedia" file, delete it (you might have to change a file manager option to Show Hidden Fiels). This should add the photos to the Gallery, but the problem is that Instagram might add the .nomedia file back in automatically. In that case, use the file manager to copy those photos to a different directory (like the main /Pictures directory).