"constantly consulting" is correct and usable in written English.
It is often used to mean that someone is regularly or regularly seeking advice or information from someone or something else. For example, "The manager is constantly consulting with other departments to ensure that the project is on track."
Dr. Johnson was a hypochondriac, constantly consulting doctors & often commenting on them in his writings.
Meyer devotes unlimited time to his new ventures, tasting every item on the menu multiple times, suggesting alterations to such minutiae as the size of a sous chef's dice and constantly consulting with the manager.
We are constantly consulting with the opposition on how they can get organized so that they're not splintered and divided in the face of the onslaught from the Assad regime.
Then, Richard, who has never mastered conversational Russian, wrote a smoother, more Englished text, constantly consulting Larissa about the original and the possibilities that it did and did not allow.
In practice, this means developing a product or service step by step, constantly consulting with customers so that money isn't wasted on features they will not want.
The host, Jim Hill, was underprepared and constantly consulted his notes.
Mr. Ballmer constantly consulted with Bill Gates, Microsoft's chairman.
PARIS — Imagine Sherlock Holmes with a cellphone attached to that pocket watch he constantly consulted.
"The library is incredibly important and constantly consulted," Ms. Cooke said.
Duke players constantly consult with one another on the court without looking to the bench for direction or approval.
Norval C. White, a co-author of the authoritative, encyclopedic, opinionated and constantly consulted AIA Guide to New York City, died Saturday at his home in the village of Roques, in southwest France.
