If my child had a blood transfusion as a child and the blood might have had sickle cell disease, could he get the disease?

No. Sickle cell anemia is not an infection and cannot be transferred from one person to another by a blood transfusion. You need to inherit it from your parents.
No. No, sickle cell disease is genetic not infectious and cannot be passed person to person, except parent to newborn child genetically.
No. Blood cells transferred to your child during a transfusion wear out & are disposed of within 3 months, usually less. There are no cells that could change your childs bone marrow into producing sickle cells. That information passes in the dna at conception, without it in the dna your child won't ever make sickle cells. It is not like an infection.

Related Questions

Is it possible that after a while a sickle cell patient body starts rejecting blood transfusions?

Not really. There's no such thing as "rejecting" blood transfusion. Very rarely, someone can have a severe allergic reaction to transfused blood, with hemolysis (which as a sickle patient you may know a lot about). But this is exactly what blood typing is designed to prevent. If you think transfusions aren't boosting your hematocrit or hemoglobin as much as in the past, discuss it with your doctor. Read more...