Site-built deck drainage
Here is an article in Fine-homebuilding on site-built deck drainage.
In this article they use EPDM rubber roofing material.
I wouldn't hesitate to use this or creative alternatives, but I wouldn't consider this as a "waterproof/roof" system. I would consider it rain-proof where it diverts rain and rain-runoff from underneath the deck.
Retail deck drainage
There are products available that are designed for this as well. Like Timbertech Dryspace for example.
My opinion
Using either a site-built or retail product, I still wouldn't store anything under there that would be ruined from getting a little bit of moisture now and then.
If you want a real waterproof roof, then build it as a code-approved roof with code-approved materials installed how they were intended to be installed.
Issues
One potential issue I can think of right off the bat is that dirt and debris will collect in there, so do you have a plan on cleaning this out? You will need access from time to time to at least stick a hose at the highest part to rinse it out.
Another potential issue is that this would limit the airflow and potentially increase the humidity between the decking and drainage material. This could contribute to things like cupping or premature finish failure on wood decking.
Real Roof (info as requested in comments)
60mil vinyl can be considered an approved roofing surface. You would use something like this if you are not putting another surface over the deck.
Another roofing option (if you wanted to add wood planks) would be to do flat roof (i prefer a torch-down roof): then build panels out of your deck surface, or attach the decking to sleepers (see image below), or use wood tiles
Sooner or later the splining will deteriorate, and whatever sealant you put in may as well. Also, you are creating little pools in the gaps that may be breeding grounds for mosquitos in wet weather.
Have you considered a waterproof underlayer instead of sealing the seams?
You could use any of various roof panels, such as pvc, polycarbonate, asphalt composition or even metal. These would only need to be sealed at their edges, a relatively few linear feet that are easily accessible from underneath. And many of them are relatively cheap.
This layer can be easily sloped and you could direct drips in whatever direction you choose.
Best Answer
I’d use 1/8” per foot slope because 1) it’s enough to actually allow water to run off, and 2) the deck will “appear” flat
You don’t want standing water on your deck. It can cause rot, etc. I live where we get a ton of rain. It’s important to get rid of water on wood, etc. on the exterior of a home.
When you look at the deck, it will appear flat AND your soup bowl will not spill when you place it on a table.