About the only such drug for which I looked for this effect and did not find it was Nexavar and its compatriot.
After hours searching there does, in fact, appear to be reasonably little regarding use of kinase profile to predict efficacy of VEGFR inhibitors. E.g. I did find one such purported paper - but amusingly (and frustratingly) it doesn't actually answer the question it says it is answering.
Purpose: No biomarkers have been identi?ed to predict outcome with the use of an antiangiogenesis agent for cancer. Vascular endothelial growth factor (VEGF) genetic variability has been associated with altered risk of breast cancer and variable promoter activity. Therefore, we evaluated the association of VEGF genotype with ef?cacy and toxicity in E2100,...
Results: The VEGF-2578 AA genotype was associated with a superior median overall survival (OS) in the combination arm when compared with the alternate genotypes combined (hazard ratio 0.58; 95% CI, 0.36 to 0.93; P .023)...
I.e. they never tested whether: a) the drug works better in that genotype, or b) whether that genotype just lives longer, despite that being the claimed purpose of the study. (and, no, this wasn't just a poorly written 'results' section - the body of the paper is no better.). Yet is still published in a reasonably high Impact Factor, peer reviewed, journal.
PS All that said, the paper does possibly highlight an aspect that might matter - that for some drugs the efficacy of the drugs may depend more on the patient's genome than the tumor's.