Are there free cloud computing platforms for biology projects?
If you're getting started with a project and need some free computational resources you should look at https://galaxyproject.org/. There are some free servers that you may be able to use. However, Galaxy is designed to have pre-fabricated pipelines and a GUI to avoid having to deal with command-line tools. Therefore any sort of custom analysis will have to go through the galaxy API.

Otherwise, most of the free computational resources that were available several years ago like iPlantCollaborative are no longer available. Running servers costs money, after all, and the funding for such projects often runs out after a few years.

You may consider asking researchers at your local universities to collaborate and provide you with access to their servers.