Irving, I am in the USA. The last royer oscillator I built ran at 5khz so I put that in as a baseline. I’d definitely be willing to run one much faster. I am not opposed to getting a transformer from China.
You'd be best advised to design your own and prototype it - using manufacturer core data and/or dev kits such as that proposed by @Papabravo. For small, sub-1kW, devices, winding your own is relatively easy for turns ratios in the order of 10:1 - 25:1 on an EI or EE core. Getting a manufacturer, such as "Custom Transformers" here in UK to make one for you is likely to be expensive as even for a prototype you're looking at a few $k for a minimum quantity of typically 10 - 50, they rarely do one-offs.
Well you need some idea of the required inductances and turns ratios, plus primary/secondary currents. If you have a working setup you could use existing transformer data as a starting point; Estimate the primary inductance from voltage/current measurements (V = -L di/dt), and use that plus peak DC and rms AC currents to give you saturated current and normal current ratings for core material saturation and primary turns calculations...
Plenty of YouTube videos if you search for them...
"Osborne" transformer company, in the Detroit Michigan area, has a large line of transformers, and will also manufacture them to your specifications. Not cheap, but certainly good quality. And if you need a few hundred transformers they could do that also.
Prior to any serious design effort you need the complete specifications, not only output voltage, but certainly output current or power. Also the input supply voltage, duty cycle, and acceptable regulation .
400 volts out with a 1:10 turns ratio implies a 40 volt supply, which is rather uncommon. And as I am not familiar with a "Royer Oscillator"circuit and whatever inductance it would require. Core saturation is always a consideration in transformer design and so the power density and material desired also add into the specification.
So a transformer design is indeed a "big deal".