You should be able to install frameworks which are statically linked. Firebase seems to be a static framework. However it also looks like Firebase is written primarily in Objective-C. To consume Objective-C code from Swift in a framework you’ll have to expose the interface (header) file to the app that will consume your framework. That could potentially lead to a conflict in if the consumer of your framework also consumes Firebase. To counter that problem you can write your own custom objective-c code that wraps Firebase and then consume your custom objective-c wrapper. You’ll have to expose your custom wrapper but at least if the framework consumer also consumer Firebase there won’t be a collision.
In the case you want to include a third party framework which is not a static library/framework your framework consumer must also embed that framework in their app. You can specify in your Podspec your framework’s dependency and Cocoapods will automatically embed those frameworks for you in the consumer app. Check out:
Hope that helps,