The incident took place at 11:20am on September 15, at the restaurant on Market Hill.
Eyewitness reports tell of two individuals, both with open alcohol containers, arguing with two members of staff and then being told to leave.
On exiting the restaurant, one of the men moved a gun from his sock into his hand. He returned ten minutes later to continue arguing.
It is currently unconfirmed whether the weapon was real or not.
Sajid Aslam, assistant manager at Buckingham Subway, said: "We had an argument over his order and I refused to serve him because he was not showing any respect, we said we wouldn't speak to him."
"After ten minutes he came back and customers in the shop had seen he had a weapon in his sock."
During the altercation, the man used a racist epithet to describe Sajid.
Becca Eggleton, who was in the shop at the time with her 14 month old son, said: "I didn't know what to do. I was enjoying my cup of tea. The argument was over something like because he was too late for breakfast.
"He bent down and heard a clicking noise, and then pulled a 'gun' out of his sock into his hand and went away.
"I said to his friend, whether it's real or safe, if I was you I'd tell him to get rid of it.
"With all that has been going on in the world at the minute, this is not what a small town like Buckingham needs."
We are currently awaiting a statement from Thames Valley Police