i would recommend some kind of microscopic or flow/NTA based analysis rather than microplate this would count all particles and labeled particles

Start by calculating the total amount of FAM-DNA in the entire sample before the separation step, and measuring the absorbance (or the fluorescence if the absorbance is too weak) of the sample using the plate reader or a spectrophotomer (or spectrofluorimeter). It may be necessary to dilute the sample at this stage.

Because a high concentration of FAM may undergo self-quenching when confined in a lipid particle, it would be a good idea to make this measurement by dissolving a small portion of the lipid nanoparticles with a detergent to release the FAM-DNA. Make sure the pH is buffered and 7 or higher, because FAM is a carboxylic acid and its optical properties are pH-dependent. Dissolving the particles in detergent is also necessary because light scattering from a high concentration of particles will contribute artifactually to the absorbance (or fluorescence).

If you have an efficient way to separate the unincorporated FAM-DNA from the lipid nanoparticles containing FAM, the second step would be to measure how much FAM-DNA is present in the total sample of particles after the separation. The measurement will be made exactly the same way as in the first step.

Divide the amount determined in the second step from the amount determined in the first step (adjusting for any dilutions that were made) to get the fraction of FAM-DNA incorporated.