The delivery is the latest unilateral move by Democrats on the panel after Republicans moved to end the committee’s probe.
A spokesman for Schiff declined to comment.
Smith's records are of interest to congressional investigators continuing to probe potential contacts between the Trump campaign - and those within the campaign's orbit - and Russia.
Attorneys for Flynn and his son have declined to answer questions from ABC News about any alleged contacts between their clients and Smith.
The Senate Intelligence Committee previously sought and received some materials from Smith’s estate last year, as part of their ongoing investigation into Russia’s 2016 election interference.
Days before his death, Smith told the Journal he was not operating on behalf of the Trump campaign.
The acquisition of documents from Smith’s estate is the latest indication that Democrats are continuing their investigation after Republicans released a report that found no evidence of wrongdoing by the Trump campaign but criticized the intelligence community and actions taken by Trump associates.
The committee’s bipartisan Russia investigation was plagued with infighting between the majority and minority, who sparred over the focus of the probe, document production and potential witnesses at nearly every turn.
In April, Democrats - who claim Republicans failed to sufficiently explore allegations of collusion between the Trump campaign and Russia - interviewed former Cambridge Analytica staffer Christopher Wylie, and claimed that he provided new information about the controversial data firm’s targeting tactics, after Facebook claimed that it harvested data from up to 87 million Facebook profiles.
No Republicans attended the meeting, according to a source in the room for the interview.