The Monastic Office for the Feast of St Mark is unfortunately not available on Divinum Officium, but it is essentially the Office from the Common of Apostles and Evangelists in Eastertide.
You can, however, find all of the relevant texts except the readings in the Liber Responsorialis (which can be downloaded for free from the CC Watershed Library).
The Invitatory antiphon (Regem Apostolorum Dominum), hymn (Tristes erant apostoli), psalms and antiphons are from the Common, (starts page 162) or elsewhere in the book (page numbers are given in the Common).
The readings for the Second and Third Nocturns are of the feast, and can be found on my Lectio Divina Blog,
This is also a rogation day when there is traditionally a procession associated with the Mass, where the Litany of the saints is sung. If there is no procession in your location, you can say these prayers privately after Lauds - and those obliged to say the Office (ie priests and religious) are required to do so.