Okay, couple things:
First: yeah, your sketches are a little bit of a mess, but you already knew that. :p
Second: where the arm curls in to meet the outer side of the chair, you've got a small straight piece. This is one of your problems. It creates a narrow face that will cause problems when you go to do a fillet on the front of the arm. On all three profile sketches, go back and delete this straight line. You can use the EXTEND function to carry the arc from the arm to meet the spline. After the loft, go back and put a fillet on this edge.
Third: when you do your loft, check the box for MERGE TANGENT FACES.
Fourth: due to the scaling in your loft, the inside faces of the chair are not tangent to each other. You can fix this either with modifying the sketches or by adding a fillet. (I tried a 10mm fillet at both edges, successfully.) Also put a fillet on the inside edge at the bottom of the chair.
After doing these things, you should be able to get a fillet to stick on the front edges. I used 10mm for the ones mentioned above, and 30mm on the front faces of the arms. Worked just fine.