"favor using" is correct and usable in written English.
It is used when a speaker or writer recommends using a certain thing. Example: I would favor using a more positive phrase in this situation.
Years later, Dad repaid the favor, using his influence to get Kevin a job.
"I favor using lots of book titles, play titles, names in the news, and so on.
Some military commanders in Iraq favor using the Uniform Code of Military Justice, a system they know well and trust.
Many political leaders favor using Japan's foreign reserves as a sort of war chest for combating the economic malaise.
Companies favor using their own stock in 401(k) plans in part because of the tax breaks.
Environmentalists support the effort and also favor using the same leverage to limit drift-net fishing farther out at sea.
While many Americans say in polls that they favor using these cells, many others have strong moral objections.
Both women are seen as liberal interventionists who favor using American power on behalf of humanitarian causes overseas.
Voters seem to favor using the surplus first to bolster Social Security and Medicare, according to a New York Times/CBS News poll this month.
The agricultural and pesticide industries favor using human subjects because such experiments yield more precise measurements of what humans can tolerate than do extrapolations from animal tests.
