I think Madison sounds the best with Lynn, but I don't really like that name. My favourite of your choices is Kailey (I'm probably one of the few on this board who will say they like this name).
I like Kailey Lynn the best. I think Kailey is unique without being "out there". I also like Madison, but would choose Kailey since it's not as popular as Madison.
Re: Girls Names?
Alexa Lynn, I guess.
Alexandra nn Alexa would be much nicer, IMO.
Not a fan of Kailey
Madison - extremely popular, very very sick of the nn Madi/Maddie
Alexa- ok, but I prefer Alexandra
They're all extremely NMS, but Alexa is the closest to "don't totally hate it."