both go well,  maybe Brynn,  by a little

I think I would go with Brynn too.

Brynn.  I prefer it on its own and like that the sounds are distinct from both Syndey and Reese.  Not that Sydney and Avery are that close, but "Sydney, Reese, and Brynn" sounds better to my ears than "Sydney, Reese, and Avery" does.

I definitely prefer the name Avery. Much more feminine. 

There's something sweet about the name going to the youngest too. 

Both go really well, but I love Brynn. I think that Sydney, Reese and Brynn sounds better than Sydney, Reese and Avery. However both are really nice names for girls :). 

Brynn it is :) 

Congrats! I personally like the sound of "Sydney, Reese, and Avery" better, but of course it's up to you!