Depends on the model of "feeling pain" that you accept. In animals, at least the more complex ones which clearly show pain as we humans experience it, there is a central nervous system, or at least a diffuse nervous system with central concentrations where electrochemical signals get sent and processed. If the "feeling" of "pain" means that there is a central processing of signals that produces a negative reaction, then plants do not feel pain because they lack such a centralized processing center.
However, plants (and even unicellular organisms) do display stimulus-response behavior that, if seen in an animal, could be identifies as a "pain" response. So, do they "feel" pain? Hard to say. The feeling part seems absent. But they definitely react to things which would cause pain in a human. They do not react in the same way as a human would, but they react.
The problem with your question turns on a simple word: the word "feel". Feel, in a scientific sense, can only be seen as a subjective response to an input. That subjectivity (unique perception of the individual) cannot be experienced scientifically. We cannot "feel" what another life form feels. We can only extrapolate from what we experience to how other things behave and presume that they behave similar to us because they "feel" similar to us. We cannot prove that.