Hi I have a American cot mattress size saying it needs a size is 1320 by 700 but other sites says it can fit a normal size mattess of 1300 by 690 The safety standards recommend the gap is no larger than 20mm if it centered in the cot, or 40mm on one side and one end of its pushed into the corner of the cot- so would it be ok to buy a standard mattress to be ok within the guidelines?

You are correct, as long as the gap is no greater than 20mm (when mattress centred) This is to prevent any risk of entrapment.

From Product Safety Australia:
Cot mattresses of the recommended size must be no more than:
20 mm from any cot side or end when centred on the mattress base
40 mm when the mattress is pushed to one side or end
https://www.productsafety.gov.au/standards/household-cots

Red Nose has the following information.
Only use a single, firm, mattress that fits snugly (within 20 mm of sides and ends) into the cot. The mattress must be flat (not tilted or elevated). Do not use cot bumpers or soft bedding as these have been associated with fatal sleep accidents.
https://rednose.org.au/article/what-is-a-safe-cot