On December 16, Halley arrives at the island of Madeira after two weeks’ sailing in company with Admiral Benbow’s squadron, and with not a “Sallyman” in sight. On the 19th, he writes a short letter to Josiah Burchett, Secretary to the Admiralty, giving an account of their arrival and of Admiral Benbow’s prompt departure for the West Indies.
(Halley to Burchett, dated 19 December 1698 from “Madera”, National Archives ADM 1/1871)

Halley to Burchett 19 Dec 1698 (© National Archives (£), ADM 1/1871)
Honoured Sr
On the sixteenth Instant I arrived at this Island togather with the Glocester, the Falmouth, the Dunkirk and Lynn frigots, under the Command of Rear Admirall Bembow. By reason of the Holydays it was not possible for the Shipps to have their Wines on board before this day, wch occasioned the Admirall to leave the Island the same night he arrived, being unwilling to waite so long. I have gotten my self dispatcht, and shall persue my Voiage with the first wind it being now Calm. I thought I ought to give their Lopps an account of our arrivall here, not finding that there were any letters left for you by the Admirall here; who left the Island in ?all diligence.
I am
Your Honours most obedt: Servant
Edm. Halley
I looked for the logs of the four ships that Halley mentions to see if they remark on the Paramore and provide more detail of the passage to Madeira, but no log exists for the Dunkirk during this period and the Gloucester‘s makes no mention of either Halley or the Paramore.
The Lynn‘s journal does notice the Paramore in this entry for November 30: “Yesterday abt 2 in afternoon we weighed in copany [sic] wth. ye Gloucester, Falmouth, Dunkirk, Paramour Pink. A very hard gale”.
While the Falmouth‘s has this rather slighting entry under December 5: “Fresh gales till morning, then moderate, took a small Pink in Tow …”.
Not yet “the famous Dr. Halley” his voyages will help him become!