Nested named entity recognition identifies entities contained within other entities, but requires expensive multi-level annotation. While flat NER corpora exist abundantly, nested resources remain scarce. We investigate whether models can learn nested structure from flat annotations alone, evaluating four approaches: string inclusions (substring matching), entity corruption (pseudo-nested data), flat neutralization (reducing false negative signal), and a hybrid fine-tuned + LLM pipeline. On NEREL, a Russian benchmark with 29 entity types where 21% of entities are nested, our best combined method achieves 26.37% inner F1, closing 40% of the gap to full nested supervision. Code is available at https://github.com/fulstock/Learning-from-Flat-Annotations.