The verses strongly indicate that not only did Avraham not give a double portion to Yishmael, he gave (basically) everything to Yitshak.
For example, right before stating that Avraham died, Genesis (25:5) states that he gave all of his possessions to Yitshak:
וַיִּתֵּ֧ן אַבְרָהָ֛ם אֶת־כָּל־אֲשֶׁר־ל֖וֹ לְיִצְחָֽק
And Avraham gave all he had to Yitshak.
The only exception to this listed is that he gave gifts to the children of the concubines (25:6):
וְלִבְנֵ֤י הַפִּֽילַגְשִׁים֙ אֲשֶׁ֣ר לְאַבְרָהָ֔ם נָתַ֥ן אַבְרָהָ֖ם מַתָּנֹ֑ת
And to the children of the concubines that Avraham had, Avraham gave gifts.
This seems to be consistent with Sarah's declaration (Genesis 21:10) that Yishmael would not inherit together with Yitshak.
Indeed, the Midrash (Genesis Rabba 61:7) illustrates the descendants of Yishmael claiming their unfulfilled due for the double portion, as the "son of the despised wife", whereupon they are told that Avraham chose to give everything to Yitshak. This affirms the implication that he did not give a double portion to Yishmael.
Although Avraham's division of his assets is listed before his death, the placement of those verses right before his death indicates that he allotted all of his possessions right before his death, and possibly distributed them. The gifts are thus not necessarily identical with the post-death distribution, but are related. The Midrash addresses the post death double portion, and indeed, conflates it with the verse about giving everything to Yitshak. This indicates that the Midrash too understood that either the verse refers to the division after his death, or that he dived everything up before his death.
In the same vein, R. Eliyahu Mizrahi (Genesis 24:10) understands based on Genesis (25:5) that he left everything to Yitshak. He asks how Avraham could have ignored Yishmael, according to the Midrashim that he kept the Torah, as he should have given Yishmael the double portion. He suggests that Avraham did so on the basis of the verse (21:12):
כִּ֣י בְיִצְחָ֔ק יִקָּרֵ֥א לְךָ֖ זָֽרַע
For it is through Isaac that offspring shall be continued for you.
Indicating that Yitshak; not Yishamel, was the rightful heir.
R. Hayyim Paltiel (25:6) asks the question as well, and answers that either Avraham transferred his possessions before his death, so he avoided the requirement to bequeath a double portion to Yishmael, or he based himself on the verse declaring Yitshak his rightful heir. Alternatively, he suggests that both Avraham and Yishamel were considered converts who sever their legal relationships with one another, so he was not obligated to leave him a double portion.
R. Yissakhar ber Eilengerg writes in B'er Sheva to Sanhedrin 91a, that Yishamel was not even included in the children of the concubines to whom Avraham sent gifts.