A primer on ordination blessings and indulgences
1. The practice of receiving a priest's "first blessing" after his ordination Mass is a praiseworthy custom, but there is no specific indulgence attached to receiving such a blessing or, for that matter, to attending a cleric's ordination Mass.
2. There is a specific plenary indulgence attached to attending a priest's first "scheduled" or "public" Mass (regardless of whether it is designated a "Mass of Thanksgiving", although it likely will be so designated), and to the first such Mass only. Enchiridion 1999, conc. 27. The celebration indulgenced here is not the same as the ordination Mass.
3. Deacons are authorized to give any blessings so listed in the Book of Blessings and several such blessings could be appropriately given by a deacon immediately after his ordination. See 1983 CIC 1169.3, and, e.g., Shorter Book of Blessings, passim, but especially the Appendix "Solemn Blessing and Prayers over the People".
4. Diocesan bishops may prohibit certain blessings from being offered (1983 CIC 1169.2 and CLSA Comm at 1403). Clergy should comply with such prohibitions, of course, but are free to discuss the policy with the proper authorities. Arguments against such prohibitions (say, those discouraging deacons from offerings blessings) are certainly at hand.
5. It would be within the authority of the arch/diocesan bishop to enrich a cleric's "first blessings" with a partial indulgence, per Enchiridion 1999, norm 7.1, although the requirement for prior Roman review of such grants, per norm 12, probably makes such an idea impractical for this year.
Read more about indulgences: Edward Peters, A Modern Guide to Indulgences (Liturgy Training Publications, 2008) 115 pages.