Pat (oh, Pat.) is sending you to:

>! SEYCHELLES

Here's how you get there:

>! First, note that, as Deusovi mentioned, the letters in the invite spell out "VIGNERE" and "REORDER" which tells you that you'll probably need to reorder the flags in some way and then find a key for the Vignere cipher.

>! Once you figure out that the flags spell out "SAILS", that's the only obvious key. So, how to order the flags?

>! [![enter image description here][1]][1]

>! Because some of the flags are not the flags in current use, it's important to identify when the flags were brought into use. I then thought the solution was to order each group of three by its earliest flag usage. For example, Kenya's group has Spain which began using its flag in 1785, so it's first. Here's where things broke down for me, though. I figured that the smaller flags would be a hint to figure out how to order the larger flags, but couldn't quite figure out how I arrived at my answer. I actually ended up [brute-forcing it][2] a bit once I got to this point, as I'd narrowed it down enough for brute-forcing to be a viable option.

>! KE = Kenya, GN = Guinea, ZW = Zimbabwe, LT = Lithuania, and PK = Pakistan. When you use "SAILS" as your key for that list of letters, you get "SEYCHELLES."

>! Reverse-engineering it a bit, I think the solution is to take the average age of each group of three flags, and then sorting by oldest to newest, that gives you the correct order.

  [1]: https://i.sstatic.net/uoXMI.png
  [2]: https://repl.it/@KristinaLustig/PrevailingLikableLocus