Is there any way to see when it will be the 7th day streak?

By keeping track of today's streak maybe?

Not that I know of, other than remembering it. Nice to get the 7 day streaks with lucky eggs. And evolution items as well.

For your first catch, and first spin of the day, look the top of the screen, You'll see 7 small circles. Note which ones get filled in.
I know my 7th day for my spins and catches always fall on Sundays.