Is there a website where people store their pickled models for others to try? E.g. different people might try different ML approaches on the iris dataset, is there a place where I can find/download models others have constructed?
On Kaggle.com, there is a datasets section. In this section, you can post or find datasets. For each dataset, you have the data, possibility to discuss about it and, of course, a list of kernels posts by the user. For instance, for the iris dataset, you have 592 kernels available.
Pickled models probably will not work on a different computer. It is also a very insecure format (see here). Rather go to kaggle.com or github.com and look for kernels/scripts that allow you to train a model on your own. Some frameworks, such as XGBoost, have a build in saving functionality with is more reliable than pickle.
For deep learning, there are a few model hubs where folks share models that are suitable for further fine-tuning or usage in given areas. None of these will be in the pickle format (from your question), but they are great resources nonetheless: