The sentence itself doesn't actually mean anything. It's nonsensical. It's just a sentence that's intended to sound funny. You can get what it's supposed to mean from the context. Slow down or we're going to have a crash. Slow down or we're going to hurt ourselves. This is an excerpt from the film's chief animator about the problems they had when they went into partnership with Dreamworks, a film studio in Hollywood. "That's not all. "Then there was the line 'Slow down ... you'll buckle my trunnions,'" said Aardman's creative director, Merlin Crossingham. "They (Americans) didn't get it. They said, 'What's a trunnion?' Who cares? It's something funny. I don't know what it is. If it sounds good, we're happy to go with it." In Hollywood a trunnion isn't funny. It's what you find in a plastic surgeon's outbox."

According to wikipedia, this is the meaning of 'trunnions': "The trunnions are the protrusions from the side of the barrel that rest on the carriage. A trunnion (from Old French "trognon", trunk) is a cylindrical protrusion used as a mounting and/or pivoting point. First associated with cannon, they are an important military development." As you might imagine, this is not an everyday English word. I had to look it up in a dictionary, and I suspect that most other native speakers would have to do this as well. Wallace is an inventor, so he'd know what it meant. I presume he's referring to parts of his vehicle which are sticking out at the sides. To 'buckle' means to deform or to go out of shape. So Wallace is warning Gromit that he'll misshape part of the vehicle if he drives too fast. Very few people watching this would know exactly what 'trunnions' are, but we'd all understand the general sense. Wallace is very fond of his inventions, and he doesn't want them to get damaged by Gromit's reckless driving.

Trunnion Joints were once used as a joint at the end of a cars drive shaft. (New mind just did a video about different drive shaft designs) I suspect trunnions could actually become buckled with excessive forces.

... and just to add one thing: The 'me' is a dialect form of 'my'. In standard English, this would be 'You'll buckle (damage) my trunnions.'