You have got to use either a centrifuge or some kind of filtration. Forming new solid phases can (and probably will!) co-precipitate Al and Fe.

Fiber filters may be a good chance at it has low cost.

I am assuming that you only have relatively small volumes of sample and you just want to separate the solids and liquid.  If so filtration is the best option and allows washing of the solids for assay purposes.

If trying to separate large amounts of slurry then separation of the solids with flocculent can be done, however this would be a precursor to filtration where the solids can be washed to remove the liquor, further recovery of liquor etc.

Flocculent types are varied depending on the solids and liquid chemistry.  Reagent vendors (BASF, etc) may supply small samples which they believe may give an acceptable separation, or if the university has a mineral processing department they may be able to help. note that thickening using flocculent will still require filtration to remove solids from the clarified liquor, or washing and filtering of the thickened solids to prevent contamination of the samples for assay.

unfortunately, I have difficulties to understand your question.

Do you want to remove the solids from the extractant solution? As said filtration would be an alternative to centrifugation, however, usually centrifugation with a normal lab centrifuge should also work. You can calculate necessary time based on expected minimum size and max centrifugal acceleration based on Stokes law. Using a flocculant to remove solids will inadvertently remove also extracted Fe and Al, at least partly.

Or do you want to flocculate the extracted Fe/Al?

Superfloc is a trademark of Cytec comprising flocculants of different chemical architecture. Depending on the task you may need cationic or anionic polyelectrolyte.