What is the key signature of F major? How many flats are in the key of F major ? Here is the answer:
The key signature of F major has only one flat : B flat (B♭)

Position of flats in all clefs
The flat is positioned according to the clefs, here is F major key signature in all clefs:

F major key signature in treble clef (G-clef)

F major key signature in bass clef

F major key signature in baritone clef

F major key signature in tenor clef

F major key signature in alto clef

F major key signature in mezzo-soprano clef

F major key signature in Soprano clef
How to find F major key signature?
If you only know the name of the key and you want to know how many accidentals there are in this key, how would you do to find the key signature? I will explain it to you:
To find the F major key signature, there are two methods: The circle of fifths or your brain .
With the circle of fifths:
Finding F major key signature with the circle of fifths is very easy, you just had to read the circle:
Major keys are in the colored parts of the circle, just find F and read how many flats they are: only one flat!
With your brain and rules of music theory:
You had to learn by heart that there is only one flat in F major.