2001 chevy malibu running rough

I have a 01 malibu and just had a engine flush and fuel system flush done on my car. I am on my second tank of gas since I have had this done and now my car is running rough. There is hesitation when stepping on the gas. I have also noticed the shifting of the trans is not happening when it should be and the engine temp is running hotter than normal. Over the last year, I have replaced the plugs, wires and the fuel filter. What could be causing this? A clogged fuel injector from the flush?

Hot engine and rough running in a Malibu of the era is suggestive of and intake manifold gasket leak. Have you checked the coolant and the oil. The levels and their quality? Check the oil cap and see if there is any crud under it. There are other possibilities too, but start here and keep posting.

I just had the oil changed and just checked the levels. the levels are good and the oil looks clean. I took it for a spin around the block and you can feel the hesitation or slipping when stepping on the gas. I just drove home on a 200 mile trip when this all began and the check engine light started to flash for about 5 seconds. I checked the owners book and it stated it will do this with a misfire. Could this be a slipping belt issue?

When the check engine light flashes it is usually a misfire. A slipping belt will not cause this.
It could be a coil, spark plug, spark plug wire, fuel injector, vacuum leak, etc…
The first thing to do is get the trouble codes read and find out for sure what the code is and post it back here. It will be something like:
P0300 Random misfire
P0301 Cylinder 1 misfire
P0302 Cylinder 2 misfire
P0303 Cylinder 3 misfire
Etc.
Places like Schucks and Autozone will do this for free.

Now the flashing check engine light changes things. It probably is a misfire, when the CEL flashes usually you are not supposed to drive the car for long if at all. Have the codes read for free. The clogged fuel injector could be one reason. By the way what was the reason behind the flush? The tranny not shifting could be related directly to the misfire, I doubt you have two different problems at the same time.

the car has 150k miles on it and my mpg was starting to drop off. I was at jiffy lube and was suckered into doing them.

I am not saying they are the reason, but I strongly suggest avoiding all quick lube places as we see case after case of problems with them. We hear far too many horror stories about them. Some may be fine, but many pay the help little, demand fast changes and that results in a high percentage of errors. Too many live by selling you something you don’t need at inflated prices.

The nature of their business model dictates problems.

Find a good local mechanic and stick with them for your needs.

Don't go to the quick lube places, even for directions.