Is the current policy of the Fed to gradually increase the Federal
funds rate an appropriate solution to the current increase in oil
prices that threatens to increase the inflation rate?

In recent years (since 1987), the average price of oil in todays
dollars has been about $25/barrel.  The very recent upward trend has
about doubled the price of gas.
As always, from here gas prices could rise or fall.  Notice that
Greenspan mentioned in his last speach that there is potential for gas
prices to fall, so it's not too far fetched.

"the average American uses about 700 gallons of gas a year"
http://bigpicture.typepad.com/comments/2004/06/have_oil_jitter.html

The cost of gas is around $2 per gallon, which means the average
American spends 700 X $2 = $1,400 on gas per year.  That is up from
$700 several years ago.  So we're talking about $700 out of $38,000
(the income per person in the US), which is about 2% (700/38000).  But
remember that this occured over several years, and it has already
occurred.  So the US has already seen this inflation.  If the price
goes up to $3 per gallon then that's another 2% inflation, but like I
stated before "gas prices could rise or fall".  Even Greenspan himself
said they could fall.

So, seeing as the inflation from gas has already happened and
Greenspan (who has a hand in raising interest rates) publicly stated
that gas prices could fall, the current continued rises in interest
are in fact to fend off inflation but probably not inflation caused by
future rises in the price of gas.

Keep in mind that a rise in interest rates today will not have a huge
effect today, but will slowly effect things over the next several
years.  The Fed has a very difficult job of predicting how fast and
how much interest rates will need to rise to keep inflation under 3%
annually.  My oppinion is that they are doing a great job as always
(since the 80s anyways).  A faster increase in interest rates would
make it even harder for them the watch the effects of the increase
over time and would allow for more error in their judgement.  In our
world of sharp ups and downs of so many factors in the economy they
will never be perfect of course, but I doubt we'll see inflation over
3.5% any year soon.

Most likely the fed funds rate is rising in order to give a cusion to
fed policy in case rates need to be lowered in the presence of a
softening of the economic conditions.  Raise them while everything is
fine, lower them if you need to make the economy stronger.  I know it
doesn't make total sense.