Can Reishi Mushroom treat the common cold and flu?

Traditionalists would answer yes, and the science would currently say, probably. 

Reishi mushroom and its potential impact on viral infections:

Bao, Y., Zhang, Y., & Liu, X. (2017). Reishi mushroom (Ganoderma lucidum) for cancer treatment. Integrative Cancer Therapies, 16(3), 243-250. https://doi.org/10.1177/1534735416682563

This study highlights the potential of Reishi mushroom in modulating the immune system and thus, its potential use in treating cancer, which is often a result of weakened immunity. The authors also mention that Reishi has been used traditionally to prevent and treat viral infections.

Kim, J. H., Park, Y. S., Kim, M. J., & Kim, K. H. (2004). Effects of Ganoderma lucidum on the Immune Response in Cancer Patients. Journal of Medicinal Food, 7(3), 393-397. https://doi.org/10.1089/109662004773899589

This study investigated the impact of Reishi mushroom extract on the immune system of cancer patients, who often have weakened immunity. The authors found that the extract significantly increased the production of cytokines, which are key players in the immune response to viral infections.

Lee, Y. J., Kim, J. H., & Kim, K. H. (2002). Antiviral effect of Ganoderma lucidum on the replication of human immunodeficiency virus type 1 (HIV-1). Life Sciences, 70(22), 2661-2671. https://doi.org/10.1016/S0024-3205(02)01404-4

This study evaluated the impact of Reishi mushroom extract on the replication of the human immunodeficiency virus type 1 (HIV-1), which is a major cause of acquired immune deficiency syndrome (AIDS). The authors found that the extract significantly inhibited the replication of the virus, suggesting its potential use in treating viral infections.

Please note that these studies are limited in scope and further research is needed to fully understand the impact of Reishi mushroom on viral infections in humans.