https://www.youtube.com/watch?v=9AN04imFDK8
Is this an Irish flute or a low whistle in the beginning?
Almost sure it’s a low whistle.
Fun fact: those are uilleann pipes further in, not anything Scottish.
It’s a long time since I watched the film, but IIRC, the complete soundtrack doesn’t feature anything Scottish.
Hollywood soundtracks are the ultimate victory of the tradition-mashing concept of ‘Celtic Music’, in that any ‘Celtic’ sound will do for any ‘Celtic’ nation. So what is the entire film is set in 13th Century Scotland? Apply a generous sound-wash of 1990s generic ‘Celtic’ and you’re away!
See also Local Hero, BBC Countryfile every time they go to Scotland or Northern Ireland, etc etc. Countryfile are amongst the worst offenders - last time I saw something on that from Northern Ireland it was soundtracked with the works of that well known Northern Irish piper … Kathryn Tickell!
I know it’s only mood-setting music rather than meant to be or claiming to be historically and ethnographically correct, but it still gets my dander up 
But … fact-checking is so hard … 
All those European orchestral instruments of diverse origin too! 
So how do you feel about all those orchestras for sci-fi, westerns, costume dramas etc.? Historically and ethnographically correct?
Now hang on a minute - are you suggesting that every space station and frontier town DIDN’T have their own symphony orchestra?
Though I agree with you, twas ever thus it seems.
Here’s the correspondent of the Morning Post and Daily Advertiser, London, getting cross over the same issue, on the 8th of November 1791:
“As an Irishman, give me leave to observe, that in the representation of Oscar and Malvina the Irish pipes are introduced; but why the piper should be habited in a highland dress, I cannot reconcile to my feelings… now, by my shoul, I tink an Irishman playing so well upon the pipes as little C——y, should not be ashamed of his brogues, and let the music give his Scotch bonnet the lie.”
The piper was a certain Denis Courtney who became well known at the time.
For more interesting stuff see: http://www.itma.ie/images/uploads/unionpipes.pdf
… why the piper should be habited in a highland dress, I cannot reconcile to my feelings…
Because the Irish national dress hadn’t been invented yet.
And that cape-thingy would prolly foul the chanter
I do believe however, that during the wedding scene, and perhaps a time or two later there were Scottish small pipes in the soundtrack. 
After it’s Hollywood…and if Tom Cruise can be Jack Reacher Mel Gibson can sure as hell be William Wallace. 
JD