Hi Sue
I'm currently undergoing chemo, and as Ken says, a lot will depend on the particular "cocktail" of drugs being used for your brother's chemo.
Chemotherapy is often administered alongside steroids, and it is these (along with the glucose used as the liquid base for some drip-fed chemotherapy) that will also affect blood sugar levels.
You don't say if your brother is type 1 or 2, but I have found that by virtually doubling my insulin (both basal and bolus) I have been able to bring my BS levels more or less back into the normal range within a few days. Obviously any drastic insulin changes should be discussed with the diabetes/cancer team beforehand, but not a lot of help if your brother is type 2.
Testing for keytones is important too, if blood sugars remain high, check with your care team for what action to take at agreed levels.
And lastly, don't be too afraid of what you may have read or heard about diabetes and chemo. I was really worried about how I would cope with the two, but in my case, I am managing better than I could have hoped for.
It's not a walk in the park, but it is manageable.