For formal writing, the use of "so" as a conjunction is, as Merriam-Webster phrases it, "occasionally condemned." In technical writing, I would say it is frequently condemned.
That being said, the use of "so" has been in use as a conjunction since before the 12th century. Merriam-Webster asserts unequivocally that use of "so" to introduce clauses "is standard."
I accept Merriam-Webster's opinion on this. Nevertheless, being standard does not say anything about whether it is good form. The question posed presents difficulties in that "am" is not really the heart of the question; it is really the acceptability of "so" as a conjunction. Therefore, an accurate answer must address two separate cases: 1) accepting so as a conjunction and 2) rejecting it and offering an appropriate alternative.
1) Accepting "so" as the conjunction, all you need to do is imagine that the "so" in the sentence is an "and," in which case the first example is completely acceptable except that the comma before so must be eliminated. The rule being: Dependent clauses (clauses without subjects) cannot be separated from the subject by a comma. The second example is perfectly acceptable as it is.
Now, you will of course say that to use so without a comma and without repeating the subject is awkward. I (and all other authorities) would agree, but it is "correct" to the extent that you fully accept "so" as a conjunction.
2) Rejecting or resisting "so" as a conjunction is easy. The more precise word to use is "therefore." Yet, you will notice that in the first example your ear will tell you immediately that you must substitute an "and therefore."
The word "therefore" is not a conjunction either (it is an adverb). You can offset it in parenthesis as in the following example:
I would prefer not to use Flash if
possible and, therefore, am looking
for suggestions.
If you want to keep "so" for whatever reason (and there may be several), then I would assert that the following is not only acceptable, but the best usage:
I would prefer not to use Flash if
possible, so I am looking for
suggestions.
In either case, the first example in the original question is, in fact, wrong. You must either remove the comma or add the subject. There is really not any question about that.
“Clause” is the correct term for “sub-sentence.” The clause without the subject “I” is a dependent clause. The clause that includes the subject “I” explicitly is an independent clause.