The lowest cost, most durable solution is going to be plain concrete. Resetting the flagstone would only be low cost if it was DIY. But to be long lasting, it needs to be mortared onto a concrete base. An alternative to concrete would be pavers on a tamped, granular base, but unless DIY it would be more expensive than concrete. I can't give a ballpark quote because there too many variables and I'm not in your area and am retired.

thank you! the stone is already mortared into concrete, hence the labour involved in removing everything is driving up the cost. What do you think about layering concrete on the stone?

There is no room to increase the elevation with a layer of concrete on top of the patio. Also, you say it is not in that great of condition -- not level on account of weathering and tree roots. Concrete on top of that will end up being the same.

Thanks y'all !

So I had another guy come in for a quote and he had some "novel" solutions to cut cost but still obtain similar outcome. option 1 was to cut off 5x5 pieces of the flagstone, install corrugated drains (do it on about 5 sites where the water logging is worse) and cover the pipes with crushed granite, then lay smaller pieces of similar flagstone (albeit newer looking) on the new drain paths. Option 2 was to do the option 1, maybe a bit more drains and cover the whole patio in marble gravel (on top of the remaining flagstone. Do these sound too good to be true (the main cost cutting is the labour involved in removing the flagstone and mortar and hauling it away, the patio does have poor access to it will need to be done manually. saves about 3-4 k, which is great right now ) the patio is about 500 sq ft.

You've identified one of the problems as drainage. Solving it is not just a matter of installing drain hardware, but figuring out where the water will go and how it will get there. We're only seeing a couple shots inside the patio, and with blinders on. The water would need to escape to outside of the patio. But where? (Any solution that requires water to rise back up to the surface in order to escape a pipe is not a good one.)

If I lived here, I would hate any solution that had exposed gravel as a finish. Sand bits would endlessly track inside the house.

Thanks! I added more pictures. The water will either runoff to the main drain or to a big grassy area outside. Most water goes there currently as well. I plan to get gutters too. The tracking in gravel did bother me but the contractor mentioned marble gravel is hard to track in. I will proceed with getting actual quotes for replacing it. Will cut down the tree roots as well. Appreciate the help.

I would add the gutters first to direct the water elsewhere, and then see if there is still a water drainage problem on the patio.

Looking at the new, and better, pictures, it looks like the flagstones were laid on a very thin (substandard) base of concrete. If you dig down down along the patio edge in a couple of places, you may be able to see. It would not break up like this if it were laid on a 3 1/2" thick slab. Bottom line, it would probably be much easier to break up and remove than if it were built right.

"... the contractor mentioned marble gravel is hard to track in." So it is definitely for drainage, not for walking on. Honestly, I cannot envision the description of how it would be used and how it would appear. (It wouldn't look good if one could see marble gravel in the finished product.) But the scheme of pipe in gravel-filled trenches sounds fraught with peril. Where do the trenches go and how does the water get out of them? Many of these drainage solutions improvised on the spot by Joe Blow Landscape Contractor are nothing more than temporary band-aids that fail after a short while. Underground collector pipes are prone to silting up and clogging. The real fix here is grading with a patio pitched such that the water can flow to an area where it can escape. If most water now goes to a "main drain" which we can't see and have no idea where it is. After the water is put in the ground, how is it going to get to the main drain then? There is so much mystery! We have no understanding of the larger lot (outside of the patio) and how water gets to it. In solving drainage problems, a person needs to understand from the source of the water (in this case the roof and patio area itself) all along the escape route to where the water leaves the property. We know none of the latter other than there is a drain and a lawn somewhere.

Instead of trying to find a compromised, band-aid type solution, I would look for ways to get a real fix done less expensively. Look into having the demolition done separately if needed. Create a plan, to scale, showing the proposed patio and even giving measurements and noting that it must drain at a specified pitch and in a direction works with the overall yard drainage flow. If a contractor can bid on specifics, he is much more likely not to add $ to cover vagaries. If you have contractors come out and all they have to bid on is "solving your problems," then they are going to be all over the map and probably on the high side. At any rate, you won't be able to compare one bid to another. If you can't create a simple plan for the patio, then it would be good to hire a landscape designer to help with that.