In my opinion, Logan is very 2000s and Finn very 2010s. Christopher, on the other hand, is classic, timeless name. I really like the suggestion of Christopher nn Kit. For me, Kit has a similar feel to Finn so I think it would be a good option for you to consider.
As far as Logan and Finn are concerned, just go with the one you prefer. Neither bowl me over but both are commonplace, standard names these days so your son will be fine with either. Be wary of saddling your son with two surnames though as it could lead to confusion growing up.
Some alliteration works - think Marilyn Monroe, Janis Joplin, Greta Garbot, Sharon Stone, Sissy Spacek, Farrah Fawcett, January Jones and so on - but I'm not sure Finn Fletcher falls into that same group. Felix Fletcher works though.
I agree that Finlay Fletcher is more promising. Finnegan Fletcher either sounds silly or brilliant - can't decide! Fintan Fletcher?
I know you didn't ask this but if you're having doubts about Finn and Declan, you might like:
Declan Fletcher
Euan/Ewan Fletcher
Rory Fletcher
Keir Fletcher
Lorcan Fletcher
Owen Fletcher
Quinn Fletcher (following on from the Glee theme...)
Noah Fletcher
Cormac Fletcher
Callum Fletcher
Colin Fletcher
Bryn Fletcher
Rowan Fletcher
But Christopher nn Kit is still my front-runner.
All the best!