I've bolded my favorites.
Anderson Rhys "Andy" - I love any "Andy" name, but I'm iffy on Rhys just because it looks like you pronounce it like "riss" even though it's pronounced like "reese".
Ashley Russell "Ash" - Though I do think Ashley is handsome, I'm not sure I would recommend actually using it on a boy just because it's become such a dominantly girl name. Nickname Ash is cute, but the S's in Ashley and Russell clash a bit.
Atlas Henry - Love love love this combo. I love the mythological story behind Atlas (Titan who held up the sky) and love the classic, masculine feel of Henry.
Calloway Scott - Calloway is a bit surname-y for my taste, but Scott is nice and they flow well together.
Darcy Graham* - For some reason I've never liked the name Darcy, but I love Graham and I think they go well together.
Flynn Garrett - This combo is really great. Love it.
Heath Calloway / Heath Tennyson** - Heath is nice but not my stylel, and both middles are a bit too surname-y for me. I like Heath Calloway a little more than Heath Tennyson though.
Hector James - This is a really handsome one. I love the underused, classic Hector and James compliments it nicely.
Kieran Apollo / Kieran Lowell** - I prefer the traditional Irish Ciaran spelling, but yours will definitely be easier for teachers to pronounce. I really prefer Kieran Lowell just because I feel like Apollo, the name of a major Greek god, is kind of a lot to give a child, even as a middle name. But that's just my opinion.
Lewis Abram - This one is handsome, and though I'm not sure I really like Louis I love Abram and they go well together.
Paris Gordon - I actually think Paris is really handsome on a boy though I wouldn't use it myself. Gordon has bad connotations for me but they do flow fairly well together.
Robin Wesley - I adore Robin on a boy. Wesley is okay, not really my style, but it's masculine enough to balance out the slight femininity of Robin and the combo flows nicely.
Wade Augustus - Yes yes yes. Wade has definitely been growing on me and Augustus has been a GP of mine ever since The Fault in Our Stars. They go fantastically together, though they're different styles it totally works.
Wren Theodore - I'm not sure how I feel about Wren in general, but I do think it could be handsome on a boy. Love Theodore. Like Wade Augustus, the one-syllable name followed by a three-syllable name makes for a great flow.
You have quite a handsome list! 
