How can I record the order of the blocks?

Assuming you are referring to randomized blocks, Qualtrics already does it for you. When you export the data click 'More Options' then check 'Export viewing order data for randomized surveys'.

DanielSpitz
You can do it in survey flow using Embedded Data:
Suppose you have 5 blocks, you can create a main embedded data which increment from the previous block and pipe it in the block 1 embedded data.
In below ex: "blocks_1_to_5" is the main used to increment using Qualtrics math operation, and the one which record data for block 1 would be "block1_order". In same way, for every other blocks create new embedded namely - "block2_order" for block2, "block3_order" for block 3 and so on..
Under Block 1:

Under Block 2 , it would look like-