Basic Economy flights (including Basic Economy Award flights) qualify for DL Amex first bag free benefit, they just need to be Delta operated and Delta marketed flights (I don't believe there are any Basic Economy awards on partner flights yet, so I presume this trip meets the requirement). There are longer haul international routes where a main cabin fare will already get you a free bag (like US - Asia/South America/Europe). The DL Amex card will not provide an additional free bag in these cases as it is a first bag free benefit only and does not stack on top of existing allowances.