I'll start off by saying I don't think there is a strong dislike, at least not at this point. They seem to be more at the stage of bickering friends than just plain disliking each other, after all they do have quite a bit of banter and they are willing to be friendly with each other even outside of the mission. However, Sam (and Bucky as well) does have some reasons to have a dislike of Bucky.
Is He Trustworthy? And They Didn't Exactly Get Off To A Good Start
Bucky's spent most of his life brainwashed as the Winter Soldier and doing terrible things. That's not always the easiest thing to forget. Even after he was freed from it in Captain America: The Winter Soldier it didn't take long before he was called right back up into it. Sam was there when both of these events happened and was almost killed by him. Even when Sam first meets the true Bucky he doesn't exactly drop it right there.
Sam Wilson: Just like that, we're suppose to be cool?
Bucky Barnes: What did I do?
Steve Rogers: Enough.
Bucky Barnes: Oh, God, I knew this would happen. Everything HYDRA put inside me is still there. All he had to do was say the goddamn words.
Captain America: Civil War
They're Jealous Of Each Other
You've got to remember that at different times Bucky and Sam have both been Steve's closest friend. Both are jealous of each other for this. Bucky because Sam got to get close to Steve whilst he couldn't and "took his place". And Sam because Bucky will always be Steve's closest friend and he will never be able to change that. When Bucky comes back all Steve wants to do is help him and get his friend back.
The Glue Is Gone
They were brought together through their closeness to Steve, now that Steve has gone they don't really have that glue that held them together. A nice analogy I saw was think of someone's best friend from school and best friend from university: they come together through their friendship to the mutual friend but aren't necessarily friends with each other. And they're always going to have some jealousness going on because of it.
Bucky Has Been Ignoring Sam
Bucky has been living his own life trying to put the past behind him and make up for some of his wrongdoings. As part of this he has been ignoring his friends, especially Sam. It doesn't matter how close you are with someone that is going to sting a bit, especially when you're reaching out to them.
Raynor: Oh, and you’ve been ignoring the texts from Sam. Look, you’ve gotta nurture friendships.
The Falcon and the Winter Soldier, Season 1 Episode 1, "New World Order"
How Well Do They Really Know Each Other?
You've also got to remember that they don't really know each other that well. Sam met the real Bucky for a few hours in Captain America: Civil War and then a similar amount of time in Avengers: Infinity War. Both were then Snapped by Thanos for five years and were brought back in the Blip. They've not really had that long together over the years they've actually known each other.