You can find the second to last flat, and that's the major key signature. Flats are easy!
For example:

The second to last flat is on G, so Gb Major.
This trick works for all of them except, of course, F Major, which has one flat:

Just remember that one flat is F Major.
For minor key signatures, you can count up six scale degrees on the major key signature, or count down three half steps. I usually count down, because for me that's easier, but it's technically more correct to view the minor key signature as starting on the sixth scale degree.
(Taken from another answer of mine from this question: Finding The Key Of A Song, which I initially misunderstood and this answer isn't relevant to it, but I am glad I left it up!)