The Secret Service, the comic that Kingsman was based on, was published by Icon, which is a label owned by Marvel Comics.
While both properties are based on comic books, they don’t necessarily take place in the same world, and so seeing a crossover would be highly unlikely.
While this doesn’t mean the two worlds are necessarily connected it does mean that Marvel themselves would get to make that call, they wouldn’t need to make a deal with anybody else.
On top of that, the Kingsman movies are a 20th Century Fox production, just like Deadpool is, so the same studio has the rights to both, making that side of the crossover easy to handle on that end as well.