The phrase "accumulate slowly" is correct and usable in written English.
It can be used when describing a process or action that takes time to gather or increase gradually.
Example: "Over the years, the funds began to accumulate slowly, allowing us to finally purchase the new equipment."
Alternatives: "gather gradually" or "build up over time."
In most new, successful negotiation relationships, positive developments accumulate slowly, creating trust, and the dialogue improves.
Ocean sediments accumulate slowly but continuously and provide records of past changes in Earth climate and ocean circulation over a wide range of timescales, from centuries to millions of years.
In "The Lay of the Land," intimations of mortality are everywhere, but they accumulate slowly, so that it is only in retrospect that you notice how thickly fatality hangs in the late autumn air.
On the abyssal plains, where sediments accumulate slowly, chemical and biological processes lead to the formation of metal-bearing coatings around objects such as the ear bones of fishes.
Damage from noise that doesn't seem all that bad in the moment — such as the music in spinning class and the buzz of a lawn mower — can accumulate slowly, harming hearing in ways that may not reveal themselves for years.
Depending on the frequency of access and since missing pieces of text accumulate slowly, this will add a significant period of time to the overall expected lifetime, as explored in the Introduction for the National Archives (Kew).
"We're accumulating slowly," she said.
The evidence accumulates slowly; despite being an emergency, it often feels very distant.
The seaward part of the initial delta is composed of muddy prodelta and seafloor sediments that accumulated slowly.
So does his sly humor, which accumulates slowly, like the toothsome crust at the bottom of a rice pot.
Hearing loss, which accumulates slowly over a lifetime, is neither painful nor disfiguring, so it goes unnoticed.
