Can you please specify what exactly you want to measure? There are many amyloid proteins with different properties.

for both alpha syuclein and amyloid beta peptides you can use UV-Vis spectroscopy to dose the peptide solution monitoring the absorption at 280nm using the relative extinction coefficient (different for aS or Ab)

I dont think UV-Vis spectroscopy useful for detection of amyloids or synuclein. Better use antibodies and screen by western blots

Congo Red and ThT assays are suitable for determining aggregation kinetics, or to stain amyloid aggregates. You cannot use them to quantify amyloids since they also bind many other kind of molecules. There is not an assay to quantify several amyloid proteins at once, since each amyloid protein has their own properties. You can use conventional methods (UV-VIS spectroscopy, bradford, etc) to quantify each amyloid protein.

I am assuming you have several amyloid proteins in your sample of unknown types and what a quantative estimation of how much protein is in the amyloid form. To do this I would try this procedure.

1. Spin the sample down gently. If the rpm is low enough, the pellet should be mostly amyloid fibers in a protein sample.

2. Break down the fibers by GuHcl, urea or some other method. Verify the fibers are broken down by light scattering or turbidity measurements. Measure the protein concentration by detergent compatible BCA. This step will probably take some trial and error.

3. Figure out the proportion of amyloid fibers vs disordered aggregates  by EM or AFM. If you are lucky it will be almost all fibers and you can assume (wt. aggregated = wt fiber). If not,, you will need to take enough images to figure out the mass-per length, fiber density, and length distribution of the fibers and disordered oligomers to figure out the wt % fibers vs. oligomers. There is some automatic software for this but I cant remember where I saw it.