I need to find vinyl transition strips for my finished basement, which consists of four slabs of concrete. The joints are a little rough, with the maximum gap being 1" and the floor levels vary from 1/8" to 3/8". Does anyone have any suggestions?

If the gaps are stable the is a floor patch and leveler that's is used for building up and uneven floor that can be feathered edge. I don't know if your floor has a sealer on it now or not. This product also even sticks to wood and it's a cement base product. You can get it at a big box store or a tile store.
I realize you are looking for vinyl transition strips but I don't know of one that can transition your bumps and gaps and different elevation heights. I'm still curious as to why Vinyl. The product is "henry" and it is in powder form and can be mixed with water or a laticrete in place of water. This what We use on the rehab job sites to level floors for another sub floor underlayment or carpet over it or setting tile. The one inch gap will take two applications. The product I am referring to is not a thin-set to set tile with, Its to level and fill in gaps to fix floors such as yours to level it. It comes in a 3lb pail and in 1lb box form
It just sounds like to me that you are trying to use "vinyl thresholds to make the transitions in heights and cover gaps.

Signed 21 Boat

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Thanks for the feedback. I should have mentioned that the floor is coloured and finished. The gaps were placed by the builder in order to minimize the incidence of cracking. That's the reason for looking for vinyl transition strip.

Oh! Ha ha So that's what the runway looks like? Ha
Depending on the gaps I would check into the pool companies around your area. The have slip in expansion strips to put into cut expansions and make transitions from floor to floor.
Now is there 1" gap in width or is it in height to another floor?
When you say the floor is colored and finished that still isn't being very specific. Does that mean a stained concrete floor?
And what part of the floor was the gaps the builder put in maybe I can still help but I need very detailed information still

Signed 21 Boat

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Thanks again 21boat. The maximum width of the gap is 1" and in some places it is as small as 1/4". The difference in heights of the cement slabs varies between 1/8" and 3/8", with the majority of the areas being between 1/4" and 3/8". The gaps were put in between rooms.

The Concrete was coloured when it was poured and later was coated with several coats of clear sealer.

I'm still guessing here the in-between rooms is this an opening and how wide of an opening? How Long are the gaps? Are they 3 foot or so long is there a door that separates the rooms and the gaps are in the center on the openings that separates the rooms?
Would a oak type low profile fit in this openings and look as a separation but yet looks like a planned application and give the rooms a defined division on the rooms and also take out the height transition problems at the same time? The very low profile threshold could be liquid nailed in and no drilling into crete.

Signed 21 Boat

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I'm trying to find vinyl transition strips too. I have installed a floating floor onto concrete an I do not want to nail down the transition strip from one flooring to the other. I see theses types of strip in business all the time. Does anyone know where to find them? Home Depot & Lowe's doesn't carry them.