Girls
Susannah Juliet Maeve 'Sunny' - I'm not a huge fan of Susannah or the nickname Sunny, but I do think this is a cute combo, and Juliet and Maeve sound wonderful with it.
Hazel Margot Wren - I love Hazel, and though I'm not huge on Margot I think it's nice sandwiched between Hazel and Wren. It also keeps the combo from seeming "over nature-y," if you know what I mean. I really like this as a combo.
Sylvie Clementine Faye - Sylvie is too nickname-y for me, but I do think it sounds less dated than Sylvia. I love Faye, and like your others, this combo flows really well and sounds quite pretty.
Rosemary Eva Grace 'Romy' - I'm not a huge fan of the nickname, but I really like this combo. The only thing is that the long E sounds at the end of Rosemary and the beginning of Eva clash a bit.
Madeleine India Poppy 'Maisie' - I'm not a fan of India or Poppy, but I love Madeleine and this particular spelling of it, and Maisie is a cute nickname.
Thisbe Harriet Elise 'Izzy' - I'm not huge on Thisbe because I feel like it is awkward to say and just has a general offbeat feel, though I do love Elise and Harriet flows nicely with this combo.
Belphoebe Scarlet Pearl 'Bel/Phoebe' - I've actually never heard the name Belphoebe before now, and I'm not a fan of Scarlet or Pearl either, Sorry 
I think Phoebe Scarlet Pearl might flow a little better, though.
Liesel Hermione Anne - After reading The Book Thief, I can't help but like the name Liesel. It goes quite nicely with Hermione and Anne.
Clio Araminta Eleni - This name has a more exotic feel to it than your others, for sure. I'm not a huge fan.
Freya Calliope Luna - This is probably one of my favorites from your list. I really love all three names, though I wouldn't be brave enough to use Calliope myself. I love love love this combo even though it has a slightly more awkward flow than your other ones due to the A's at the end of Freya and Luna.
Juniper Frances Scout 'Juno' - I love Juniper, but greatly dislike Scout and am indifferent towards Frances. I do think this flows okay, though.
Tessa Ramona Jane - Tessa is very pretty, and I've always loved Jane and other one-syllable classic names in a second middle name spot. I'm not huge on Ramona and I feel like the A's at the end of the first two names in this clash.
Boys
Archer Felix Jude 'Archie' - I really love this combo and all three names in it. It flows really well, too.
Henry William Jack - Another handsome one, and again, I love all three of these names. Definitely my favorite from your list.
Hector Frederick Jay - It's not my style, but I do think this works well. It does, though, remind me of Hector "Zero" Zeroni from Holes if you've ever read/seen it.
Oscar Matthew James - I'm not a huge fan of Oscar, but it does go nicely with the very handsome Matthew and James.
Avery Atticus Leo - Finally, someone who likes Avery on a boy! I could never see it fitting a girl after reading about the brother named Avery in Charlotte's Web. I think this is a handsome combo.
Hugo Rafferty Max - I don't really like Rafferty or Max, but I absolutely adore Hugo.
Edmund Elliott Miles 'Ned' - This is surprisingly cute. I've always felt like Edmund sounded a bit stiff but the nickname Ned (though it's a bit dated and Eddy would be cute) loosens it up a little and the combo flows pretty well. I love Elliott, though I tend to spell it with just on T at the end.
Spencer Cohan August 'Penn' - I'm not huge on the nickname, and Cohan is okay, but I love August and Spencer. This flows well as a whole.
Sylvie and Faye are so pretty too. they all go nicely togehter
Haha! The combo is lovely. I love Jude a lot too!
