I've read several things about covering the tefilin shel yad :
- covering it with the tallit while fixing it
- covering it with the tallit for the entire tefila
- covering it with the shirt sleeve for the entire tefila
- covering it with the jacket sleeve for the entire tefila
It seems that different sources are linked to kabbalah and the fact that it is not proper to pray with a bare arm or with a jacket sleeve hanging down
Do you have some details about those points ? Also I have noticed some rabbanim don't seem to pay attention to those things for example Rav Ovadia Yossef shlita. Thanks.
He pretty much says to cover the Tefilin with the clothing (see Birke Yosef 27:5 and Kesher Gudal 3:12). 