I noticed under the paint the wood looked blotchy almost and not even so I tried sanding it down but it didn't go away unfortunately.
I don't think it would be possible to get rid of this so there would probably be no point in attempting to sand further. Some woods are naturally prone to being blotchy, and any piece of wood can exhibit this to some degree if the grain is irregular.
My plan was to stain them using a walnut color stain to try and match a sideboard we have.
In the absence of painting the chairs again — which would give the most uniform result with the least effort — going dark is probably your best bet for an attractive end result.
My worry is the stain will just make the blotches look worse.
That's a legitimate concern with conventional stains which are intended to be absorbed by the wood and you already know the wood is problematical.
So instead of using conventional stain it would be advisable to use so-called gel stain. These aren't stains per se but instead coloured varnish that has been thickened to some degree for ease of application and to give them better covering power1.
They are easy to use and quite forgiving (e.g. of wood that was previously finished) so it's relatively easy even for a first-timer to get good results, although I would still highly recommend watching a few videos2 before attempting your first chair to get comfortable with the overall method and so you will be sure to have all you need on hand before you begin3.
Stripped of paint and sanded, your chairs are likely not to require any further prep work, although it is possible sanding lightly one last time with a coarser grit than you previously ended with might be beneficial — be advised by the specific product you buy.
In addition to the "gel stain" you'll need a clear finish for protection, again be guided by the brand you buy. However, as a rule you can use almost anything you like on top if you leave the stain to dry for a suitable period.
1 Many makes of "gel stain" are now available, and in a good range of colours, and while I won't recommend anything in particular I would caution that Minwax is generally the cheapest available for good reason.
2 There are numerous helpful videos on various channels on YouTube and a quick search will give you lots to look at. Two quick plugs: Dashner Design & Restoration uses the product quite frequently, so, many of his videos will feature its use and as a 'regular Joe' his content is very accessible; the finish manufacturer General Finishes have quick, to-the-point videos on all their major products.
3 I'm not sure if all manufacturer instructions will specify, or how much emphasis they'll put on it, but you'll want plenty of paper towels or rags on hand for wiping away excess. They can also be used for application, although you can apply "gel stain" with just about anything including your fingers (not joking, but obviously with gloves on). Note: as an oil-based finish, care needs to be exercised with any rags/paper towels soaked with it after use — lay them flat to dry, when stiff you can dispose of them with the rest of the garbage.