Check Engine light flashes and car vibrates

The only scenario I am familiar with that causes a blinking or flashing Check Engine Light is misfires. Your description of the car shaking is another sign of possible misfires as well. There could be other issues, it would be helpful to know what codes are getting set. However, with the flashing check engine light and the shaking of the car the first thing I would do, if it hasnt been done in a while, is a tune up. Replace the plugs to start. I believe you have a distributorless ignition meaning that you have coil packs instead of a distributor.

Your coil pack sits on top of the plugs. Look to the left side of the engine, just at the bottom of the valve cover and you will see (assuming you have the 4.0L 6-cylinder engine) a series of three humps. Those three humps is your coil packs and there should be four bolts that hold it in. Take out those four bolts, pry up the coil pack and then you will have access to replace the spark plugs.

While your at it, Id replace the fuel filter, air filter and other general maintenance/tune up items like that.

I have actually had this happen to me. It first started last winter, and it took me a couple of months and a few no-starts to figure out what it might be. I don't know where you live, but if you are in a climate where the gas stations change their fuel blend from summer to winter blend, this is probably your problem. My jeep was having starting problems after I had been driving and after checking my codes from the check engine light, all I could figure out was random misfires. I replaced the plugs and the same thing kept happening. I decided to change gas stations and went to a BP. They didn't change their fuel blend to winter mix, and my jeep has run great ever since. That would be my first suggestion to you...find a gas station that you don't normally use or one somewhere that doesn't change their blend, and see if your jeep will run normally again.

Have any of the mechanics used a scan tool to check for engine trouble codes? If not, bring it to a parts store, where most will do it as a free service. Write down the codes, ask what they mean and what to do to fix the problem. If u have any further questions, u can post them here. Oh, and if the mechanics didn't scan for trouble codes, find a new mechanic. Let me know how u make out.

Try what Kate said (an excellent suggestion,even if you wouldn't think your choice of gas station would matter..it DOES,stick to good name brands) but I will add, if it doesn't improve, these '01's are known for having fuel pump issues, and if your not getting a consistent pressure you'll have to drop the tank,and change it our{along w/the filter which is in there also},use a high quality replacement,such as Bosch(had good luck w/theres}
BEFORE you do that though,I'm going to include a ground guide I got from a Jeep forum,unfortunately I can't post pictures w/it.You'd be surprised how many times its just a simple ground problem,just foxed an intermittent problem on my '00 by that.---

1. I'd also freshen the engine grounds as all electrical life starts with solid grounds.
----------------------------------------------------------------------------------------------------

Spark: 12 volts from ignition switch to the ASD relay; when the key is first turned on the PCM provides a ground to the ASD relay to energize it, then the ASD relay passes 12 volts to the coil primary side. If no crank sensor signal is generated after a couple of seconds the PCM cuts the ground to the ASD relay (and fuel pump relay too) and that cuts power to the coil (and fuel pump). Key to START and once again the PCM energizes the ASD relay. Now, a critical element is the crank sensor--no signal from the crank sensor and the PCM won't trigger the coil to provide spark.
-----------------------------------------------------------------------------------------------------

Grounds can be the root cause of many electrical gremlins. Refreshing grounds is NEVER a bad idea, and the investment of your time in this procedure is always well worth it!

You can't tell much of anything by looking at ground connections!! You must remove, scrape, clean until shiny the cable/wire ends and whatever they bolt to. Be sure to remove all paint from any ground connections.

Start with the one on the back corner of the head, and where it attaches to the firewall, as it deteriorates over time and is an area that makes it susceptible to damage. Best to replace that woven cable with a #4 or #2 gauge cable. You can attach the one end to the intake manifold if you would like.

Next go over to the engine dipstick tube stud. Remove the nut and clean the wire ends and scrape the block until shiny at the stud. Reattach tightly.

If you are so inclined, add at least a #6 cable from the negative terminal of your battery to one of the bolts on your radiator support.