If you are able to play a "regular" transverse flute, you should be able to play a fife. The smaller flute, the smaller the embouchure. Only a tiny circular--not oval--opening in your lips is needed. When you find the "spot" John was referring to, if you stand close to a mirror & watch as you play, you will see a little "V" of moisture on the mouthpiece just under your lip.   

Not to sound ridiculous but, have you looked inside it? I once found a piccolo which had been in an attic for decades, and was completely closed in with moldy gunk. What fun it was to clean it out!