Grading: God willing, this hadith is sahih, and this chain is hasan in corroborating chains and supporting reports on account of Musa bin Ya'qub al-Zam'i.
Technical note / Defect ('illah): He has also been corroborated, as is made clear in "Sunan Abi Dawud". Abu Hazim refers to Salamah bin Dinar al-A'raj.
Reference / Source: Abu Dawud (2540) recorded it through al-Hasan bin Ali, from Sa'id bin Abi Maryam, with this same chain, and it will come again later under number (2566).

Technical note / Defect ('illah): It has been narrated from Malik, and there is disagreement among those narrating from him over whether it is mawquf or marfu', as explained in the annotation on "Sunan Abi Dawud"; those who narrated it as mawquf are more numerous.
Reference / Source: In Malik's "al-Muwatta'" (the narration of Yahya al-Laythi, 1/70) it is mawquf on Sahl bin Sa'd (may Allah be pleased with him): "There are two times at which the gates of heaven are opened, and seldom is a supplicant's supplication rejected: when the call to prayer is given, and when lining up in ranks in the path of Allah."
General principle: Something like this cannot be said on the basis of personal opinion; it must necessarily be based on a transmitted report (i.e., it takes the ruling of marfu').

Corroborating chains and supporting reports: This narration has been reported from Malik by three routes as "marfu'" (as a saying of the Prophet (peace and blessings be upon him)), the most sound of which is what Ibn Hibban (1720) recorded by way of Abu al-Mundhir Isma'il bin Umar (al-Wasiti) from him as marfu', with the wording: "There are two times at which the gates of heaven are opened: when the prayer is due, and when lining up in ranks in the path of Allah."

Technical note / Defect ('illah): There was disagreement among those narrating from the narrator (Sulayman bin Tarkhan) al-Taymi over its chain and over whether it is marfu' or mawquf, as al-Daraqutni explained in "al-Ilal" 12/91 (2460), and he said: "The correct view is that it is mawquf."
Reference / Source: For the full takhrij of this hadith of Anas (may Allah be pleased with him), see "Musnad Ahmad" 19/(12200), where it is narrated as marfu' by way of Mu'awiyah bin Qurrah from Anas.

Details of the narration: As for the narration of Burayd bin Abi Maryam from Anas, it too is with Ahmad (20/12584), and it is marfu' with the wording: "Indeed, supplication is not rejected between the adhan and the iqamah, so supplicate."
Grading: Its chain is sahih.