Having two vowel sounds in a row does not hinder the pronunciation of French but the fact that when you say

quelle école  
/kɛl   ekɔl/

you only hear one vowel sound is explained by the fact that the letter “e” at the end of “quelle” is not sounded. Usually the final “e” of a word is not sounded in French unless it is the only vowel in the word. (As in “le”).

Therefore feminine

quelle   
/kɛl/

is pronounced the same as masculine

quel   
/kɛl/

When you pronounce “quelle école” you do not pronounce the letter “e” at the end of “quelle” and the vowel “é” is pronounced /e/ at the beginning of “école” making a liaison with the preceding /l/ sound.

It is the same with a word starting with a different vowel sound

quelle activité   
/kɛl   aktivite/ 

Your confusion might arise from the fact that sometimes in French we elide the “e” for pronunciation purposes, such as at the end of “le” and “de” when the next word begins with a vowel sound:

• le arbre l’arbre
• la orange l’orange
• je ne veux pas de oranges d’oranges

In French as spoken in the north of France and in particularly in Quebec, the letter e at the end of a word does not always call for a vowel sound. If you listen to one of these speakers you will not be able to tell the difference between quel [kɛl] or quelle [kɛl] nor between seul [sœl] and seule [sœl], among many other gender dependent examples. It can however become a vowel if too many consonants are around, usually starting from 3 or more, like in notre liberté. It’s realization can be anything between a mid-central vowel [ə] or a rounded [œ] or [ø], but in any case it is never stressed. Some speakers also tend not to add any vowel at all and drop liquid consonants instead: /’nɔtʁ(ə) libɛːʁte/ is pronounced [nɔt libɛːʁte], arbre /aʁbʁ(ə)/ is pronounced [aʁb], etc.

Your example quelle école does not contain long clusters of consonants and is therefore simply pronounced [kɛl‿ekɔl]. Only one vowel is heard between the two words.

The pronunciation is approximately the same in the south of France and in Swiss and Belgian varieties of French but for different reasons. In these regions there is a perceptible difference between quel [kɛl] and quelle [‘kɛlə] or seul [sœl] and seule [‘sœlə], etc. Notice again that the stress is never on the final /ə/ and that its realization is close to a mid-central vowel [ə]. This sound is so neutral that it is disappears completely if any vowel comes before or after. The only perceivable change could be the length of the vowel. It is reported that this length difference is somewhat noticeable in Swiss and Belgian pronunciations.

Quelle école could therefore be pronounced [kɛl‿eːkɔlə], with a still single but slightly longer vowel. Diphthongs are reported in the Swiss variety when the /ə/ comes after the vowel, but in this case I don’t think a diphthong ever occurs (please comment if you know about this).

Everything about these /ə/ is explained in French here:
http://www.projet-pfc.net/le-francais-explique/le-e-muet