There is no need to convert these vectors to angles to compute a rotation matrix. All you need to compute a rotation matrix in 2D are the cosine and sine of the angle and you already have them encoded in the direction of the difference vector. You indeed simply have to normalize the difference vector:
(cos(angle), sin(angle) ) = normalize(P2 - P1).
If you think you have to compute the angle to compare them between different fingers positions, then it is not true again. If P3 and P4 are different positions of your fingers, then you can compute the cosine and sine of the rotation angle between the two vectors by simply using a complex division. If do not know complex numbers I suggest to learn about them, but you can implement the division using the following formula:
(a, b) / (c, d) = ( a*c + b*d, b*c - a*d ) / (c*c + d*d).