Why is the flag of Prague yellow and red?

It seems somewhat coincidental. According to this page about Prague flags:

Historic City of Prague Flags

In 1784, the Austrian Emperor Josef II by Imperial decree incorporated the four separate towns of Prague ( Old Town, New Town, Lesser Town and Hradschin-Castle ) into one city ruled by a single Magistrate. The Magistrate offices were located in the Old Town hall and the arms and flag of Old Town became those of a new capital. The Old Town flag then consisted of two horizontal stripes, black and yellow, which were the colors of the municipal arms in 1622. Unfortunately, they were identical with colors of the Habsburg dynasty which made the Prague "landesfarben" not very popular among Czech citizens.

In 1886, the Municipal Council asked the painter B. Wachsmann to paint new municipal arms, colors and seals for Prague, which he did making the new colors of Prague yellow and red. Since that time, a horizontally divided flag of yellow and red has been considered the official municipal flag of Prague. The new flags in those colors became symbols of Prague and were first used extensively for the Jubilee Exhibition of 1891.

This flag is sometimes confused with the traditional flag of Moravia. The colors used on the flags are simply "coincidental" and based on the heraldic rules used when making flags from the colors of coat-of-arms. Other than the colors, they are not related.

The City of Prague is actually made up of almost 100 small towns that were absorbed as the city grew. Today, the towns have become districts, each with their own unique flag.

I take it that by "based on the heraldic rules used when making flags from the colors of coat-of-arms" the page's author means the heraldry rule whereby you're supposed to interlace colors (that is, green, red, blue, etc.) with metal (gold or silver) so that colors only touch metal and vice versa. If memory serves, black and white could be used as either color or metal.

There's a bunch more historical flags on this other page from the same site, which notes in passing on the 1477 old town flag's entry that:

In 1477, the Bohemian King Vladislaus II divided the flag of Old Town into three stripes of red, yellow, and white replacing the older black and yellow of the Hapsburgs.

Put another way, and as you'll see viewing the flag pictures, the gold/red theme in the flag has been around since the middle pages and doesn't seem to be tied to the Habsburgs outside of not wanting to use the latter's black/gold theme. And the current pick of flag in 1886 appears to be a simple matter of an artist applying heraldry best practices.

There might be more/better sources in Czech that go into the precise meaning of the gold/red pick, why this design in particular, etc. Be wary if look outside of Prague for explanations if you research this deeper, because one locality's explanation for a pick of color and design often is different from another's.

I would like to try answer this question. According to this article which is unfrotunately only in Czech:

From the main colors of the emblem, the colors of the Prague battalion were derived in the 19th century. In the following years only the accompanying pieces of the emblem change, the shield itself has remained unchanged up to the present.

The reason why it was chosen by Prague's mayor in 1991 is because the red and yellow flag can be use for free, without of permission from the Prague town hall.

The historical flag is much more interesting. The appearance come out from attributes from 14th century. There are three turrets with gate and wall. The colour of the turrets was silver but for the help Frederick the third it was changed to gold. Only the battlements stay silver.

The hand with sword was add by Ferdinand II as acknowledgement for Prague to successful defence against the Swedish army in Thirty Year War.

So this possibly can answer this question. The colors is really common in Bohemia country attributes.