As water metaphors, "stream", "trickle", and "pour" can work fine together, as long as you set up the metaphor correctly. To trickle suggests a slow stream of water of minimal volume, while to pour suggests a much larger stream and volume.
The rain trickled from the roof of the house in a slow, steady stream.
The rain poured from the roof of the house, washing away all the debris that had accumulated in the gutters.
You are on the right track, but your metaphor is inelegant. Sensors collect data, much like rain gutter, but they do not store data. You need some kind of storage device for that, in the same way you would need a barrel to store up water. Since you don't mention the storage device, it makes the reader question what you mean.
You should also consider that pour is commonly a transitive verb, meaning there is some actor who intentionally pours the water from one place to another. For example:
He poured her a cup of lemonade.
You would not say
He trickled her a cup of lemonade.
If the data pours into the phone, then what is the mechanism that decides when this happens? It makes more sense to say it is poured implying some (unspecified) actor.
The water trickles through the gutters into the rain barrel, where at regular intervals it is poured into the cistern.
Lastly, you should consider common idiom. You may have heard of "data dumps". "To dump" is the common idiom to describe moving large quantities of data. It doesn't really continue the water metaphor, but, since you can "dump" water, it doesn't break it either.
The data trickles into the sensors and is stored in internal memory. From there, at regular intervals, it is dumped to the phone.
(Edit) as Lambie's comment mentions, there is a time and place for metaphor, usually with creative writing. When writing product documentation, it's better to be matter-of-fact.
The sensors receive small amounts of data over time which is stored (somewhere). (A monitoring process) then dumps this data to the phone (when certain criteria are met).
Metaphor would be fine in an article about the software. Still, as I first said, you have to properly set up the metaphor.:
The developers explain that the sensors get a constant trickle of data from hundreds of sources. Once certain criteria are met, this entire pool of data is poured into the end-users' phone for analysis.