Sink drains into dishwasher? I think you mean the dishwasher drains into the sink tailpiece (or the garbage disposer if you have one).
Most codes require an air gap to be installed in such connections. Most codes also require equipment to be installed according to their listing and labeling information (which you will not have) and in accordance with any manufacturers instructions (your installation instructions). Usually, the codes state that the manufacturer’s instructions apply when there is a conflict between the code and the instructions, i.e., the equipment was accepted for use by the code based on its listing and labeling, the listing and labeling includes the manufacturers instructions. I stated this in the long, explanatory form so you will understand the following statement.
Most dishwasher installation instructions specify the drain line be installed over the top of the dishwasher before being connected to the sink drain, but do not REQUIRE an air gap be installed. The drain line running over the top of the dishwasher is to reduce back siphonage from the sink into the dishwasher and to reduce back siphonage when the sink backs up.
If your dishwasher’s installation instructions state to run the drain hose over the dishwasher and does not require an air gap, an air gap is not needed.
If your installation instructions refer to ‘if required by local code’, typically this falls back to the manufacturer’s installation instructions which do not REQUIRE an air gap.
That was a long way to say that you probably do not need the air gap. If you did, one would likely have been provided with the dishwasher for connection to the drain line.
I am sure there will be many follow up comments by others, but this gets down to what is required by the code and typically the manufacturer’s instructions rule, according to that code.