The f-droid app actually handles google play/amazon store links via the 'open with' dialog, so if it's installed deep linking should already work.
What F-Droid needs (maybe it already has these things too?) is:
1) It's own URI schema for these things - so that you can link directly to F-Droid without a Google Play link. So https://f-droid.org/repository/browse/?fdid=in.p1x.tanks_of_... should take you to the app if F-Droid is installed, otherwise you should be prompted to download it from the web page.
2) A way to deep link into the app when it's not installed... so that if the user downloads and installs the app, the first page they see is the one they wanted to see (e.g. a particular app).