There are different groups of Karaites, and the general rule is that all opinions are accepted and are subject to equal scrutiny. To quote from Karaite Korner's FAQ section: https://www.karaite-korner.org/karaite_faq.shtml
"If you interpret the Bible then don't you have your own Oral Law?
No. An Oral Law would imply that we claim that a given set of interpretations were bestowed upon us through a prophecy which was not included in the Hebrew Bible. Not only do we not make such a claim, but **we believe that every interpretation must stand up to the same objective scrutiny, regardless of its source**.
How can you have a community if everybody interprets the Bible themselves?
This is only a problem if we start off with intolerance. Karaites have learned to have tolerance of greatly varying interpretations as long as they are derived from sound principles of Biblical exegesis and only based on the Tanach. The reason for this tolerance is that we know that it is more important to do the right and moral thing than to do the same thing as everyone else."
Therefore, some Karaites wear Tefillin, some don't. The Torah only says to bind an "os" (sign) on your hand and a "totefos" between your eyes. Tefillin is the oral aspect of the same law. Since the Karaites reject being "bound" to oral law, they interpret as they wish, and in some cases go based on Rabbinic interpretation.
On the note of Tefillin, the same site Karaite Korner states that as a general rule, they don't wear Tefillin:
"Do Karaites wear Tefillin (phylacteries)?
No. See http://www.karaite-korner.org/tefillin.shtml
But I thought Karaites wear Tefillin between their eyes?
This is not true. See: http://www.karaite-korner.org/tefillin.shtml.
How can Karaites know how to make Tefillin if the written Torah doesn't tell us how?
We can not know how to make Tefillin from the Torah because Tefillin were only invented by the Rabbis 1500 years after the Torah was given. The Torah commands us to treasure the commandments as jewels, not to strap leather amulets onto our heads and arms."
Anecdotally, it's ironic that it was "invented by the Rabbis 1500 years ago" when Tefillin in "amulet form" was excavated from the Qumran caves, showing evidence that it's much older. See https://www.chabad.org/multimedia/media_cdo/aid/1591202/jewish/The-Tefillin-of-Qumran.htm