Do we have WoB that indicates that squires don't have spren?
I'm not sure that they do but I do think that it's a possibility. We haven't seen any indication that the guys from bridge 4 have spren but when Syl first started following Kaladin around, and he first started using stormlight, there was also very little if any indication that he had a spren.
It's been indicated that many of the spren have been hesitant to return and bond with humans because of the recreance but I think they might have overcome that. I think that because of the night that Syl freaked out before the attack by Szeth. I assume she freaked out because Odium has returned and I would imagine that the other spren know it too. I think that would scare them all and that it would be enough to force them to cross over and bond with humans again.
I think that the difference in numbers of squires between the Radiant Orders are due to the number of spren, so there would be many honor spren and therefore many Windrunner squires but few Bondsmith spren and therefore, most of the time, no Bondsmith squires.
Historically squires are knights in training and up until the end of WoR Kaladin would've been a squire. A squire without a knight to train him, unless you count Syl, but still a squire.
Also, about flying:
"There is an art, it says, or, rather, a knack to flying. The knack lies in learning how to throw yourself at the ground and miss."