Sounds like the US reseller takes ownership of the goods in the UK and therefore is required to register for UK VAT.
Going through your process :
The Supplier delivers goods and services direct to End User - Czech Republic to UK
Goods are shipped from Czech to UK end user but the importer of record is you, the UK distributor.
The Distributor, us, are billed by the Supplier, we are also classed as the importer and are charged import duties and VAT.
Supplier will issue zero rated invoice to you (distributor) and as you are the designated importer of the goods, you become the owner of those goods. We know you are the owner of the goods because the Czech company have invoiced you for the goods. You will either be charged the import VAT by the freight agent or more likely the freight agent has your EORI number and will put the import VAT you are liable for/owe to HMRC, to your postponed import VAT account (PIVA), if you do not know about PIVA then see this link https://www.gov.uk/guidance/get-your-postponed-import-vat-statement
Don't focus on the physical movement of the goods, there is only ONE physical movement (Czech to UK end user), but there is more than one change of legal ownership of those goods and for VAT we look at these changes of ownership as much as we look at the physical location of the goods...and this is perhaps why you are struggling with the answer...you are looking just at the goods and not the ownership chain.
The Distributor invoices US based Reseller
As you are the importer of record, you take ownership of the goods in the UK (confirmed by Czech billing you for the goods)....you then sell these goods to the USA, so although the goods have not physically moved from the UK location (the end user where the goods were delivered directly to), the ownership has changed hands twice, firstly from Czech to you in the UK and secondly when you sell to the USA.
You cannot zero rate the sale to USA because to zero rate it, you need proof of export, as the goods are not leaving the UK, you will never have proof of export. So you'd charge UK VAT to the USA reseller.
US based Reseller invoices UK based End User
USA reseller acquires goods in the UK (from you) and makes an onward sale of those goods to a UK customer, as the USA company is not a UK established company, then the VAT registration threshold is Nil, the £90k threshold only applies to UK companies. USA companies registers for UK VAT, charges UK VAT to end user and can also reclaim the VAT you charged them so USA are not out of pocket.
1. As a Distributor invoicing US Reseller for this order, would we be charging UK VAT?
Yes, because you own some goods in the UK, you are selling them to a customer in the USA but the goods are not leaving the UK, without proof of export, the sale is standard rated. Section 6 here https://www.gov.uk/guidance/get-your-postponed-import-vat-statement
2. How would the End User account for VAT, if any?
The end user will probably get an invoice from the USA with no VAT on it because the invoice will be wrong, but think about it... it should not be possible for a UK company to buy goods that are in the UK, VAT free. If end user went to PC World or Harrods and bought the goods they'd be charged VAT but here, because the supply chain is broken, the end user is obtaining goods VAT free.
All you can do is protect your own position, as you are not exporting the goods then you cannot zero rate the goods to USA, the USA will not like that but then this whole supply chain should have been figured out before the transaction took place. On what basis would you zero rate your sale to USA if you are not exporting the goods?
You cannot assume this post is entirely correct nor constitute advice, all depends on the details but from what you describe the supply chain/flow does not appear to be correct, if you have an Accountant then probably a good time to speak with them or if this is going to be a regular transaction, speak with a specialist freight consult who can set this up in a much more efficient manner for longer term benefits.
The services aspect of the transaction - you stated the Czech sells both goods and services - services different rules for VAT but depends what those services are, if they are for example of installation services then there are different rules to if the services are say "software support", so its not possible to answer this question but in theory if Czech sells "services" to you and you sell to USA and USA sells back to UK then these could all be under reverse charge rules.
