Is there a chemical test for gluten?
Gluten describes a subset of proteins (glutenins and gliadins) found in wheat grain and making up a large fraction of the protein found in common wheat flour (&gt;70%). Since the protein fraction of wheat flour can represent &gt;10%/wt, the gluten fraction commonly represents &gt;5%/wt of the flour.
Given the requirement for an easily implemented chemical test this eliminates more advanced and regularly used methods such as immunoassays (eg ELISA), and maybe even dye-binding assays such as described by the AOAC Official Method 2011.04.
One frequent chemical method to measure the amount of protein in a food sample is known as the Kjeldahl method, which detects nitrogen (which is absent in the carbohydrate). Other assays for nitrogen would also do the trick.
Büchi manufatures equipment for performing the required assay (Ref. 1), and provides an application note based on standard method AOAC 920.87. Although it is unlikely that you will have a Büchi SpeedDigester K-436, K-439, or Kjeldahl Sampler System K-370/K-371, available in your school lab, you'll still require the chemicals and equipment for performing a high temperature digestion and distillation, which should be similar to that listed in the application note. Note this is not a simple experiment.
Unfortunately the Kjeldahl method is likely to be difficult to implement in some educational laboratories given the required equipment, chemicals and experience. An alternative family of less challenging methods to determine protein are biuret methods (BCA and Lowry assays, which exploit protein-copper chelation and secondary detection of reduced copper), as described for instance on the ThermoFisher Scientific website. These however employ absorbance measurements to determine the amount of chelated or reduced copper.
If you are looking to distinguish gluten against a background of other proteins, you may have to isolate the gluten fraction (see eg Ref 2.). In general your approach would depend on the expected concentration and amount of gluten in the sample. Since this is a question about an educational application, it is assumed that you are not concerned with a non-gluten protein background or with detection of low concentrations.
References

Büchi Application Note 027/2010. Nitrogen and Protein Determination in Flour according to the Kjeldahl Method.

Ravinder Kaushik, Naveen Kumar,Manvesh Kumar Sihag, and Aradhita Ray. Isolation, characterization of wheat gluten and its regeneration properties. J Food Sci Technol. 2015 Sep; 52(9): 5930–5937.
doi: 10.1007/s13197-014-1690-2