Well designed applications provide the user a path and design a journey where he begins and completes his/her task following few steps. If you are designing a journey, you may not want to provide two doors (which are side by side) when both lead to the same passage. Considering that, I wouldn't favor the idea of keeping two controls which perform the same function and both are available right on the same screen at the same level.
Benny has mentioned multiple assess points which is a nice feature but my interpretation of multiple entry points is that they should exist at different levels so that users with different navigational preferences be able to begin their journey. In that sense, placing something on the screen is one level and a second level could be placing the same command in a context menu. But in your case, if you put two icons at two locations on the same screen, you are still using the same level and this doesn't qualify to be a "multiple-entry-point" approach. Also for Mobile Apps, I wouldn't be too keen to use multiple entry points as real-estate is scarce resource and you wan to use it as economically as possible.
Concluding: I wouldn't want to put a bottom navigation on the Home-screen.