#You can attune up to 3 items
The Basic Rules covers this (my emphasis):
An item can be attuned to only one creature at a time, and a creature can be attuned to no more than three magic items at a time. Any attempt to attune to a fourth item fails; the creature must end its attunement to an item first. Additionally, a creature can't attune to more than one copy of an item.
As long as they aren't the same item, a character can attune to up to 3 items. Your character can definitely attune to both the Cloak of Protection and the Staff of Fire (assuming you also meet the requirements for the Staff).
##But can you attune simultaneously? No. Unfortunately, you are limited to just one item per short rest. The same section of the basic rules linked above covers this (emphasis mine):
Attuning to an item requires a creature to spend a short rest focused on only that item while being in physical contact with it (this can't be the same short rest used to learn the item's properties).