Expression analyses can be simply done by Western blot (semiquantitative) or ELISA (quantitative) analyses. Adequate antibodies are offered by Abcam etc (e.g. see: https://www.abcam.com/products?keywords=VEGFR), ELISA solutions are also available (e.g. see: https://www.biocompare.com/Search-ELISA-Kits/?search=elisa+vegfr).
I think you have first to confirm that your inhibitor acts only on VEGFR. because many of VEGFR inhibitors exhibited inhibitory activity against other tyrosine kinases. this could be attributed to the similarity between its active site with the active sites of several TKs. Most of the approved inhibitors have dual/multi-kinase inhibitory activity.
If you are sure that your inhibitor acts only on VEGFR? the WB, ELIZA, cell culture could solve this problem.