No ,the miles aren't interchangeable and can't be mixed and matched.

Diners allows two types of transfers miles-to-points and points-to-miles.

Only UA and AA participate in miles-to-points. For these transfers, 1 mile = 1 Diners point. This represents a loss of 50% of the value of the original AA or UA mile, because, under the points-to-miles scheme, 2 Diners points usually equals 1 mile. Many airlines participate Diners CR points-to miles.

Now, during the Diners/BA points-to-miles double promotion, 1 Diners point (instead of the usual 2) = 1 BA mile. This rate restores to value of the original AA or UA mile to 100%.

So, if you want to combine miles from UA, AA, and/or BA, you first need a Diners club card. Then you transfer from any AA or UA accounts you or your family members have into your Diners account. Then, before the promo ends on 8/31, you transfer the points to BA miles. This bigger, single balance allows you to get better awards like concorde of international first class.