The definite article is accepted, but the indefinite one is better.
For me, the sentence suggests that it is a jacket not known to everyone.
If it were "Hledám červenou bundu." then it could be said by a child to their mother and the mother knows which jacket is the "červená bunda", but in the sentence here it is more likely just describing the colour of a jacket (perhaps found by the speaker).
One can always stretch it. We can imagine the list of things being sought by someone. And you might ask Who is looking for the red jacket? Most likely it would be "tu červenou bundu" if "the" is meant but in the right circumstances we cannot exclude just "červenou bundu".