You use paired commas to set off a parenthetical.
Findings show that there is increased blood flow to the brain.
If you want to insert "during the initial stages of love" as a parenthetical, you set it off with commas, hence:
Findings show that, during the initial stages of love, there is increased blood flow to the brain.
This has nothing to do with the fact that the parenthetical happens to be preceded by the word "that". For example:
Findings show, during the initial stages of love, there is increased blood flow to the brain.
Findings show, during the initial stages of love, that there is increased blood flow to the brain.
Notice the commas are still there, still setting off the parenthetical. These are a bit awkward, but still perfectly legal grammatically.
