In parshat Vayechi Yaakov blesses (almost) all his children. There is no mention of him giving a blessing to his daughter Dina. I would like to know if there is any recording of a blessing from Yaakov to Dina or, if not, is there an explanation as to why he didn't bless her?
This site says yes, through her marriage to Shimon.
Dina did get blessed from Ya'akov. Dina married Shimon (see Rashi Vayechi 46-10) therefore the bracha that was given to Shimon (see Rashi 49-28) was like giving her a bracha also.
the son of the Canaanitess: The son of Dinah, who had been possessed by a Canaanite. When they killed Shechem, Dinah did not want to leave until Simeon swore to her that he would marry her - [Gen. Rabbah (80:11)].
Ralbag writes the following at the end of Parshas Vayechi:
רבים יתמהו מזה לפי שכבר ימצאו מבניו שלא ברך אותם כמו הענין בראובן ושמעון ולוי עד שהוכרחו לומר שכבר ברך אותם איש כברכתו ולא נזכרו אלו הברכות ואולם מה שנזכר מזה הוא מה שהודיע אותם מה שיקרם באחרית הימים
Many have been astounded by this, for we already find that he did not bless some of his sons, as is the matter with Reuven, Shimon, and Levi. To the point that they were forced to say that he had already blessed them, each one in accordance with his blessing, and those blessings are not mentioned. But what is mentioned here is what he informed them about what will occur to them at the end of days.
Though he goes on to disagree with this, according to this interpretation the Torah does not mention the blessings of anyone. It is thus possible that Dinah was blessed along with everyone else.