Can I fly to the UK with my Schengen Residence Permit?

As a national of a non-EU country, you will need your passport to enter the UK.

You have said that you are from Africa. If you are from Namibia or Botswana, you do not require a visa to enter the UK.

If you are from another country, you do require a visa to visit the UK. Your statement to the contrary appears to be from the official summary, but it is nonetheless incorrect. In fact the freedom of movement directive says, at Article 5(2)

Family members who are not nationals of a Member State shall only be required to have an entry visa in accordance with Regulation (EC) No 539/2001 or, where appropriate, with national law.

In this case, since the mentioned regulation concerns the Schengen area, which does not include the UK, the requirement is according to national law.

(I have reported the error in the summary.)

If you are traveling with your spouse (or to join your spouse) then the appropriate document is an EEA family permit, which is free of charge. (Otherwise, you need a standard visitor visa for most purposes.)

However, the advice to drive to the border is not as crazy as some people here seem to think. At Article 5(4), the directive says

Where a Union citizen, or a family member who is not a national of a Member State, does not have the necessary travel documents or, if required, the necessary visas, the Member State concerned shall, before turning them back, give such persons every reasonable opportunity to obtain the necessary documents or have them brought to them within a reasonable period of time or to corroborate or prove by other means that they are covered by the right of free movement and residence.

What this means in practice is that if you can get to the border, you can present evidence of your marriage to the border officer and, if the officer accepts the evidence, you should be admitted. There is some anecdotal evidence here that this has happened.

The problem is that you cannot do this when traveling by air, because an airline will not take upon itself the uncertainty over whether the officer will accept the evidence of your relationship. The airline will board you only if you have an EEA family permit or other acceptable document.

It would be less risky to apply for the EEA family permit before your journey. If you have time, you should consider doing that.

You mention Article 10. Article 10 does not apply to you unless your German residence permit says Aufenthaltskarte für Familienangehörige eines Unionsbürgers. Under most circumstances, the spouse of a German national living in Germany would not have such a card. If your card does nonetheless say that, then you do not need an EEA family permit; instead, you can look at Entering the UK as the holder of an Article 10 residence card to see what you need to enter the UK.

The requirements for entering the UK are the same, whatever means of transport you use, so whether you come by plane, train or car is entirely up to your personal preference.

The airlines use a system called Timatic to find out what documents you will need. It's crucial for airlines that this database is accurate and that they check it properly, because they get fined if they carry somebody without the correct documentation and have to take them home again. Obviously, mistakes can happen, but it's very unlikely that an airline would refuse to let you board if you have the correct documentation.