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BMX / mid BBs are a royal pain, steer clear
While I wouldn't necessarily agree with this, the cranks you'll be forced into using will make life difficult.
The single bolt attachment that bmx cranks use doesn't lend itself well to the forward and backward forces that fixed riding exerts. You could go spline drive but chainring availability in sizes large enough to give you a sensible gearing isn't going to be good and spline drive chainrings are $$$ compared to normal 4/5 bolt rings.
I'd have a good think about rear spacing. I have a 135mm spaced frame built fixed (with a 6bolt hub/cog) and to be honest, it's a kludge. I could throw money at it and have it set up better but at the moment I have spacers behind my chainring and I've spent some time making it work well but I was converting an existing bike to fixed. If I was starting from scratch and riding fixed was my goal, I'd definitely be going 120mm at the rear end.
imo your best bet is to buy a cheap as chips 26" mtb frame on ebay or suchlike, then get horizontal dropouts put on by a framebuilder.
BMX / mid BBs are a royal pain, steer clear