VAT is linked to the supplies of services, so you do need to be certain who is supplying what to whom. The fact that the app store is only paying the other company implies to me that the only supply of services that you’re making is assisting the other company with the development. It doesn’t sound like you have any direct contractual link to the app store or app users?
If I’m right about the structure, where is the other company based?
If it’s in the UK, then the income is likely to be subject to VAT (assuming you’re over the £85k threshold). If the other company is VAT registered, it shouldn’t be a problem to them, as they’re likely to be able to recover the VAT from HMRC on their VAT return, based on a VAT invoice that you issue them. If it’s only them that knows the amount due, you could even enter into a self-billing arrangement which would allow them to draw up the VAT invoice on your behalf – see HMRC’s notice 700/62 https://www.gov.uk/guidance/self-billing-notice-70062
But if the other company is based overseas, you need to determine what the place of supply is for VAT purposes. This can depend on exactly what is being supplied, and you should refer to the guidance in HMRC’s Notice 741A https://www.gov.uk/guidance/vat-place-of-supply-of-services-notice-741a. If the place of supply is the UK, it will be liable to UK VAT, as above. However if the place of supply is deemed to be overseas, the other company may be liable to account for a similar tax there.