If a non-Jew does an act which would be considered a kiddush Hashem or chillul Hashem if done by a Jew, does it have the same status?
Kiddush/chillul Hashem taken to mean showing the world that this is how Hashem's chosen people behaves:
No, by definition: The gentile cannot be representative of a group he does not belong to.
Kiddush/chillul Hashem taken to mean letting one self be killed rather than doing something for which one is required to let oneself be killed rather than doing:
Yes, by definition (at least theoretically): If that is the label of an act, and he did that act, then it has that label.* (However, as per Sanhedrin 74b, there may not be any actions requiring a gentile to sacrifice his life, rendering occurrence impossible.)
* My head spins from reading my own words!
In the Yerushalmi in מסכת שביעית פרק ד הלכה ב we learn the following:
רבי אבונה בעי קומי רבי אימי: עכו"ם מהו שיהו מצווין על קידוש השם? אמר ליה: ונקדשתי בתוך בני ישראל ישראל מצווין על קידוש השם, ואין העכו"ם מצווין על קידוש השם! ר' נסא בשם ר' אלעזר שמע להן מן הדא: (מלכים ב ה) לדבר הזה יסלח ה' לעבדך וגו' ישראל מצווין על קידוש השם ואין העכו"ם מצווין על קידוש השם.
Rabbi Avuna asked Rabbi Eimi: ""Can a non-Jew perform a Kiddush Hashem?
He answered: [The Pasuk in] (ויקרא כ"ב-ל"ב) says וְנִקְדַּשְׁתִּי בְּתוֹךְ בְּנֵי יִשְׂרָאֵל - I will be sanctified within the Bnei Yisrael; Beni Yisrael are commanded to sanctify His Name, and non-Jews are not commanded to sanctify His Name.
R' Nisa in the name of R' Elazar learnt it from here: [When Na'aman takes leave from Elisha HaNavi, he promises not to worship idols anymore. However, he says] לַדָּבָ֣ר הַזֶּ֔ה יִסְלַ֥ח ה' לְעַבְדֶּ֑ךָ בְּב֣וֹא אֲדֹנִ֣י בֵית-רִמּוֹן֩ לְהִשְׁתַּחֲוֹ֨ת שָׁ֜מָּה וְה֣וּא | נִשְׁעָ֣ן עַל-יָדִ֗י וְהִֽשְׁתַּחֲוֵ֙יתִי֙ בֵּ֣ית רִמֹּ֔ן בְּהִשְׁתַּחֲוָיָ֙תִי֙ בֵּ֣ית רִמֹּ֔ן יִסְלַח-(נא) ה' לְעַבְדְּךָ֖ בַּדָּבָ֥ר הַזֶּֽה - that when he the King of Aram goes to worship idols, while leaning on Na'aman's arm, Na'aman will bow with the king and not risk his life.
Elisha does not object, but says וַיֹּ֥אמֶר ל֖וֹ לֵ֣ךְ לְשָׁל֑וֹם and approves. No concept of a non-Jew performing a Kiddush Hashem .
Now, if a non-Jew were to sacrifice his life for a Kiddush Hashem, he would essentially be committing suicide. Suicide is part of Murder that is forbidden to all of mankind, as Noach was commanded וְאַךְ אֶת דִּמְכֶם לְנַפְשֹׁתֵיכֶם אֶדְרֹשׁ.
Rav Ephraim Oshry (Shu"T Mima'amakim 2:4) mentions briefly that it's a Machaloket Rashi, Tosafot, and the Rambam. (Thanks to @DoubleAA for the source) Rav Ovadia (Yabia Omer vol. 6 Yoreh Deah 13:12) cites a number of Acharonim - Meshech Chochmah and Maharatz Chayut included - who write that although Bnei Noach are not obligated in Kiddush Hashem, they are permitted to give up their lives at will in such situations.