DIY Servo arm using wrong inverse kinematics doesn't make a straight line
It sounds like the servo velocity is not being properly controlled. 

Can you slow the arm movement down? 

Remember, for inverse kinematics to work properly, you need very precise control of the rate of rotation. If your system has the arm moving from one point to another at the maximum possible velocity, the servos may be hitting their maximum rotation speed. As such, one servo would complete its motion before the other, which would turn your line into a series of arc segments, that are partially blended together.

Try controlling the system so the arm moves to points in an X-Y coordinate system. If the arm can correctly move the pen to the specified points, it's a servo-speed issue. If not, it's something else.