Plan on some help. Two people could do it but 3 would be easier. Beer buddies are good for this kind of job.
The plan that I suggest keeps everyone above the beam during the lift so an accident is not likely to kill someone. It is your plan if you adopt it, so you can modify it any way you want.
I assume that since you are remodeling the kitchen, a hole through the floor might be acceptable.
I would bolt the channels together before lifting because you might have troubles lining up the holes; but your choice.
Get some light chain (you are going to be lifting half the beam at each end) and put a hole through the kitchen floor large enough to pass the chain. One hole near each end.
Fasten a chain to the beam at each end of the beam. Have two pins (maybe 3/8" rod) to put through the chain where it comes through the floor up in the kitchen.
If you have two strong helpers, you can simply put a handle on the chain, have two of them lift, and put the pin through the chain where it comes out of the floor. It will be easiest if the pin rests on two pieces of 2x4 where the chain comes out of the floor.
Lift about 6" at each end alternately so you don't get a lot of tilt in the beam.
If you don't have strong helpers, you can make a lever with an 8 ft 2x4 with a hook that will easily connect to the chain. Put the hook about 18" from one end. Then one guy can lift while another inserts the pin in the chain.
Leave the chains in place while you set the jack posts.
It may cost a little more but I would use two of the adjustable steel jack posts to finally support the beam. They have pin adjustments and a screw adjustment for the final couple of inches. You will appreciate the jackscrew when the you have to adjust it. I would not trust 2x4s and shims to hold up my new kitchen. If you use 2x4s, get your structural engineer buddy to design the column.
I assume that the beam is supporting the midspan of the joists. It is VERY IMPORTANT that the bottom of the beam and the top of the post be braced laterally to prevent sidewise motion so the bottom of the beam doesn't "kick out" and dump the whole thing on the floor. If one of your buddies has a welder he could weld the beam to the column when you get it all installed.
The beam will provide the greatest stiffness and strength, and minimum sag, if the posts are located in from the ends by 20% of the length of the beam. If it is a 13 ft beam, the optimum point is about 2.6 ft in from each end.
You must make sure that the footing is adequate. Some basement floors are less than 3" of concrete without reinforcing and a post could just punch through the floor. If there is no designed footing under the post, then you could put pressure treated plank under the column to spread the load.
The adjustable posts will be useful when you get settling or shrinkage of lumber.