there are several possibilities:-by using a 3D digitizer working at low radio frequency, like polhemus;- by making a gravity clinometer using a goniometer with a long needle  tied to angle dial and a plumb-line for the zero;- by taking a picture from above the canopy with a gimbal and by relating the image to calibratio pictures at different angles, that are  made with flag leaf replica in dark paper.., 

Now a days the most accurate method used by most researchers are ,First of all they design the angles on white sheet paper then using that white sheet paper for measuring different types of angles

ROTFL :)

By the way, the problem is very interesting but often neglected.

Blade angle is driving ligth interception and a growing angle relative to sun increases the radiative flux. A piece of paper does not have all the information for azimuthal angle of leaves, which is necessary to relate them with sun elevation but can be a broad sense indicator for selecting open or close vegetation types. I assume that coarse phenotyping is better by taking a picture from a potted plant seen by side against a frame or in the field, by % of ligth absorbed.

It is normal to take the culm as the main axis form which to take the angle of inclination. When I worked with raspberry that what I did and it worked out well.

If you just need to get an idea about the flag leaf angle, you can refer  IRRI descriptor status of rice. You can easily download it from IRRI website. But it doesn't  give the degree of angle.