No, plants do not feel pain. They do not have a nervous system, they do not have consciousness, etc.

Even if they did, that's still an argument for veganism. Where do you think animals get the energy they store in their bodies? They don't absorb it from the sun. They eat plants, use some of that energy sustaining their life, then you eat them and absorb some of what's left. Anywhere from 1/4 to 1/10th of the energy they originally consumed. Meaning if you are looking to minimize suffering, regardless of whether or not plants feel pain (which they don't), eating plants directly is how you do that.