Taking klonopin as needed may very well ease some of the withdrawal symptoms, especially the RLS, insomnia, and shakiness. Because klonopin is in a different class of drug than kratom, however, it will not alleviate all the side effects - you will probably still have some flu-like symptoms and sweatiness.
A doctor knowledgeable about opioid addiction and who is familiar with kratom might prescribe a small quantity of a weak opioid, which would help more than klonopin would. It will be rather difficult to find such a doctor in the United States though; kratom isn't a widely known substance.
Of all the opioids you could become dependent on, kratom has a pretty benign withdrawal profile. Be glad you're not dependent on oxycodone.
Best of luck to you, and use the klonopin only as needed. It can be habituating as well, so be careful with it.