Yes and no.
You can have skills with the same modifier which would stack to your attribute.
But 2 +1 fight cards would only add +2 to your current fight number on your slider. You only ever get 1 additional die per clue token (unless you are Joe Diamond..or perhaps another expansion character as well I am not familiar with). Fight skill has nothing to do with clue token additions.
Read the fight skill card more carefully. It has two effects. One is a passive +1 to all fight checks, the other effect is that you get an extra die when you spend a clue.
And yes, OP, both effects stack.