The KJA Siddur appears to have a number of instances of influence from the Rabbinic liturgy. Some examples of note, based on a brief perusal:
Page 2: The brachah on tzitzis. (The questions there being 1. what is their (non-rabbinic) source for a brachah, and 2. why is the text of a brachah --שם ומלכות, אקב"ו--virtually the same as Rabbinic brachos?)
Page 6: Text at the beginning of and in between every line of the Kedusha that does not quote directly from the text of the praises of the Malachim in the Navi. (The question there being that the purpose of kedushah is specifically with regard to the verses that the Malachim say--the question can, in fact, extend to the source of the Kedusha, which seems to be Rabbinic based on that Gemara.)
Page 7: A verse in between the verse of Shema and the following paragraph of Ve'ahavta. (If the section is quoted straight from the Torah, there should be no verse in between Shema and Ve'ahavta--it seems to be rooted in the Rabbinic liturgical structure of including Baruch Shem Kevod).
Is there a documented Rabbinic influence on Karaite liturgy, and if so, how does the Karaite community reconcile this influence in their prayer when (as I understand it) they largely reject Rabbinic influence?