This is tricky and techniques range from simple Archimedes to complex pycnometry..  a textile engineer generally talks in terms of denier & tex which are measures of density.

For my opinion helium pycnometry is the method of choice for determination.

Follwing article will be helpful:

M. Truoga et al. "A comparative study on natural fibre density measurement",

J. Text. Inst., 100 (6), 525–529 (2009)

You may also check answers to a very similar question: https://www.researchgate.net/post/How_do_I_find_the_density_of_natural_fibers

Hi,

you need the weight of fibers in two different phases. first, the weight of dry, and second, the weight of wet fibers. both of which, can be gain by specific balance or scale. If you need more information, contact me buddy.

Because of the unique structure, surface morphology and hydrophilic nature of natural fibers, measuring their density is a challenge. 

Depending on type accuracy that you are looking for, there are two methods of measurements. 1- gas pycnometry 2-Archimedes method. 

1- Gas pycnometry is an acurate method of measurement, but might not be available to you. you can use either Nitrogen or Helium.

2- Archemedes method is simpler and you can do it in any lab set-up which is availabe to you. you can follow the procedure for density measurements usning submersion method. BUT there are differences when deadling with porous materials and especially natural fibers:

2-1) the liquid or the media that you are using is very important in your final results. for Flax fiber either soybean oil, or canola oil is recommended. our experiments and reserach have shown that using mentioned oils will provide the best results comapred to gas pycnometry. 

2-2) for better results you have to use vacuume chamber. after measuring dry weight of your fiber, and after submersion, place your container with fiber in it under vacuum pressure for 5-10 minutes ( pressure over -70kPa is recommended).

2-3 make sure that you condition your fiber before doing the measurements. moisture content. usually drying your fiber in the oven for 6-10 hours is recommended.

Please do not hesitate to contact me if you had any questions.

Easy method..Use a Density Balance..Accurate density u can find..But u need a immersion liquid if the density is less than 1..weight in air and weight in liquid..this methods gives the digital reading

U can try with methanol displacement method or helium pycometer method..